Find the perimeter of each compound shape in this math worksheet.

Let’s solve each problem one by one. Remember, the perimeter is the total distance around the outside of a shape. We just add up all the side lengths!

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Problem 1:
Sides: 14 cm, 14 cm, 5 cm, and two more sides that are not labeled — but wait! This is a pentagon (5-sided shape). The diagram shows:
- Left side: 14 cm
- Bottom: 14 cm
- Right slanted side: 5 cm
- Top right slanted side: ?
- Top left horizontal: ?

Actually, looking again — it looks like a rectangle with a triangle on the right? But no labels for top or top-right. Wait — maybe it's symmetric? Or perhaps we’re missing something.

Wait — actually, in many such problems, if only some sides are given, you assume the rest can be deduced from symmetry or by completing the shape.

But let’s look carefully:

It appears to be a house-like shape: rectangle + triangle on right.

Left vertical = 14 cm
Bottom horizontal = 14 cm
Right slant = 5 cm
Top right slant = also 5 cm? (if symmetric)
Top horizontal = same as bottom? 14 cm?

Wait — that would make it a pentagon with sides: 14, 14, 5, 5, and then the top must connect back — but if left is 14 and right has two 5s, the top might not be 14.

Actually, this is tricky without more info. Let me re-express:

Perhaps it’s a trapezoid? No.

Wait — maybe the figure is made so that the top edge equals the bottom minus something? Not clear.

Hold on — perhaps I misread. Let me check standard approach.

Actually, in worksheet problems like this, often all outer edges are labeled except where they match others. But here, only three sides are labeled: left=14, bottom=14, right-slant=5. That’s not enough unless we assume symmetry.

Wait — maybe the top-left horizontal is equal to bottom? And the top-right slant equals the right-slant? So:

Assume:
- Left: 14 cm
- Bottom: 14 cm
- Right slant down: 5 cm
- Right slant up: 5 cm (symmetric)
- Top: 14 cm? But then the shape wouldn’t close properly.

Alternatively, think of it as a rectangle 14x14 with a right triangle attached on the right side, base 5 cm? But height?

This is confusing. Maybe I should skip and come back.

Wait — let’s look at Problem 2 instead — clearer.

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Problem 2:
L-shaped figure.

Given:
- Left vertical: 21 cm
- Top horizontal: 11 cm
- Inner vertical drop: 11 cm → so the right part starts 11 cm down from top
- Then inner horizontal: 10 cm
- Then right vertical: 10 cm
- Bottom horizontal: 20 cm

We need to find all outer sides.

Let’s trace the perimeter clockwise:

Start at top-left corner:

1. Go right: 11 cm (top of left block)
2. Go down: 11 cm (inner vertical)
3. Go right: 10 cm (inner horizontal)
4. Go down: 10 cm (right vertical)
5. Go left: 20 cm (bottom)
6. Go up: 21 cm (left side)

Wait — but when we go up 21 cm, we’re back to start? Let’s check if that closes.

Actually, after going left 20 cm along bottom, then up 21 cm — yes, that brings us back to top-left.

But is that correct? Let’s verify the heights.

Total height on left is 21 cm. On the right, we have a segment of 10 cm going down, and above that, there’s an 11 cm drop — so total height on right side is 11 + 10 = 21 cm — matches.

Widths: top part is 11 cm wide, then extends 10 cm more to the right, so total width should be 11 + 10 = 21 cm? But bottom is labeled 20 cm — inconsistency?

Wait — bottom is 20 cm. Top has 11 cm + 10 cm = 21 cm? That doesn’t match.

Ah — here’s the key: the “inner horizontal” of 10 cm is not adding to the width — because the bottom is 20 cm, which includes the entire base.

Let me draw mentally:

The full shape:

- From top-left, go right 11 cm → end of top bar.
- Then down 11 cm → now at the "corner" inside.
- Then right 10 cm → now at the top of the right-bottom rectangle.
- Then down 10 cm → bottom-right corner.
- Then left 20 cm → bottom-left corner.
- Then up 21 cm → back to top-left.

Now, check horizontal consistency:

From left to right at the bottom: 20 cm.

At the top: first segment 11 cm, then after dropping 11 cm, we go right 10 cm — so the total width from leftmost to rightmost point is 11 + 10 = 21 cm? But bottom is only 20 cm — contradiction.

Unless... the 10 cm inner horizontal is overlapping or something.

Wait — perhaps the 20 cm bottom includes the projection.

Alternative approach: use the fact that for rectilinear shapes, opposite sides can be matched.

Total height = 21 cm (given on left).

On the right side, we have two segments: 10 cm (lower) and 11 cm (upper), summing to 21 cm — good.

Total width: bottom is 20 cm.

Top has a segment of 11 cm, and then after the step, another segment — but how long is the top-right horizontal? It’s not labeled.

In L-shapes, sometimes the missing side can be found by subtraction.

For example, the full width if it were a rectangle would be max(widths). Here, the bottom is 20 cm. The top-left part is 11 cm wide. The part that sticks out to the right — its width should be such that when added to the left part, it makes sense.

Actually, the horizontal distance from left to the inner corner is 11 cm. Then from there to the right edge is 10 cm — so total width is 11 + 10 = 21 cm. But the bottom is labeled 20 cm — that’s a problem.

Unless the 20 cm is a typo or I'm misreading.

Looking back at the image description: for problem 2, it says:

"2) 11 cm (top), 11 cm (down from top-right of left block), 10 cm (right), 10 cm (down), 20 cm (bottom), 21 cm (left)"

And the shape is L-shaped.

Perhaps the 20 cm bottom is correct, and the top-right horizontal is not 10 cm additional, but rather the 10 cm is the length of the arm.

Let’s calculate the perimeter by adding all visible outer sides.

List all outer edges:

- Left side: 21 cm
- Top side: 11 cm
- Right side of top block: 11 cm (down)
- Top of bottom block: 10 cm (right) — but this is internal? No, in L-shape, this is exposed if it's the top of the lower part.

I think I need to visualize better.

Standard way: for an L-shape made of two rectangles, the perimeter is the sum of all outer sides.

Assume the large rectangle is 21 cm high and W cm wide, but cut out a rectangle from the top-right.

From the labels:

- The left column is 21 cm tall and 11 cm wide.
- Attached to its bottom-right is a rectangle that is 10 cm wide and 10 cm tall? But then the total height would be 21 cm, and the bottom part is 10 cm tall, so the top part must be 11 cm tall — which matches the "11 cm" label going down from the top.

So the shape consists of:

- A left rectangle: 11 cm wide × 21 cm tall
- A bottom-right rectangle: 10 cm wide × 10 cm tall, attached to the bottom of the left rectangle's right side.

But then the total width at the bottom is 11 + 10 = 21 cm, but the diagram says bottom is 20 cm — conflict.

Unless the 20 cm is the length of the bottom side, which should be 11 + 10 = 21 cm — so probably a labeling error, or I'm misinterpreting.

Perhaps the "20 cm" is the bottom, and the "10 cm" horizontal is not additional width.

Another idea: the 10 cm horizontal is the length of the protrusion, but the bottom is 20 cm, so the left part must be 10 cm wide? But it's labeled 11 cm on top.

I think there might be a mistake in my reasoning or in the problem.

Let's look for a different strategy. In many worksheets, for such L-shapes, you can calculate perimeter by noting that it's the same as the perimeter of the bounding rectangle plus twice the depth of the notch, but here it's not a notch, it's an extension.

Perhaps add all given sides and see what's missing.

Given sides in order around the shape:

Start at top-left:

1. Right: 11 cm
2. Down: 11 cm
3. Right: 10 cm
4. Down: 10 cm
5. Left: 20 cm
6. Up: 21 cm

Now, does this close? After step 5, we are at bottom-left, then up 21 cm to top-left — yes.

But the issue is that the horizontal distances don't match: from left to right, at the top, we went 11 + 10 = 21 cm, but at the bottom, we went left 20 cm — so the net displacement is not zero, which means the shape isn't closed properly.

Unless the "left 20 cm" is not the full bottom, but that doesn't make sense.

Perhaps the 20 cm is the length from the right end to the left end, but since the top is wider, it's impossible.

I recall that in some diagrams, the numbers are placed on the sides, and for L-shapes, the missing side can be calculated.

Let me denote the points.

Let A be top-left.

A to B: right 11 cm

B to C: down 11 cm

C to D: right 10 cm

D to E: down 10 cm

E to F: left ? cm — but labeled 20 cm

F to A: up 21 cm

For the shape to close, the net horizontal movement must be zero.

From A to B: +11 cm (right)

B to C: 0 horizontal

C to D: +10 cm (right)

D to E: 0

E to F: -X cm (left)

F to A: 0

Net horizontal: 11 + 10 - X = 0 => X = 21 cm

But the diagram says E to F is 20 cm — contradiction.

Similarly, vertical: A to B: 0

B to C: -11 cm (down)

C to D: 0

D to E: -10 cm (down)

E to F: 0

F to A: +21 cm (up)

Net vertical: -11 -10 +21 = 0 — good.

So horizontally, it should be 21 cm for the bottom, but it's labeled 20 cm. Probably a typo in the problem or in my reading.

Perhaps the "20 cm" is correct, and the "10 cm" horizontal is not 10, but let's check the image description again.

User said: "2) 11 cm (top), 11 cm (down), 10 cm (right), 10 cm (down), 20 cm (bottom), 21 cm (left)"

And in the text, it's written as "20 cm" for bottom.

Maybe in the actual image, the bottom is 21 cm, but typed as 20 by mistake. Or perhaps I need to proceed with the given numbers.

Another possibility: the 10 cm "right" is not horizontal, but that doesn't make sense.

Or perhaps the shape is not aligned that way.

Let's assume that the bottom is 20 cm, and the top has 11 cm, and the difference is made up by the steps.

In that case, the horizontal segment between the two vertical drops might be shorter.

I think for the sake of time, I'll assume that the bottom is 21 cm, as per calculation, and proceed, or use the given numbers as is.

Perhaps the 20 cm is the length, and we have to accept it, and the perimeter is sum of all given sides.

So sides are: 11, 11, 10, 10, 20, 21

Sum: 11+11=22, +10=32, +10=42, +20=62, +21=83 cm

But is that correct? Only if those are all the outer sides, which they are, in sequence.

And even though the geometry might be off, for the purpose of this worksheet, we add the labeled sides.

So for problem 2, perimeter = 11 + 11 + 10 + 10 + 20 + 21 = let's calculate: 11+11=22, 22+10=32, 32+10=42, 42+20=62, 62+21=83 cm

Okay, I'll go with that for now.

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Problem 3:
Rectangle with a bite taken out of the top-right.

Given:
- Left side: 19 cm
- Bottom: ? not labeled, but probably same as top or something.
Labels: 18 cm (top-left horizontal), 16 cm (top-right horizontal), 16 cm (right side), 19 cm (left side)

So, likely, the shape is a rectangle with width = 18 + 16 = 34 cm, height = 19 cm, but with a rectangular notch removed from the top-right.

The notch has width 16 cm and height? The right side is 16 cm, but the full height is 19 cm, so the notch depth is 19 - 16 = 3 cm? But not labeled.

To find perimeter, we need all outer sides.

Trace the boundary:

Start at top-left:

1. Right: 18 cm (to the start of the notch)
2. Down: ? — this is the depth of the notch. Since the right side of the main shape is 16 cm, and full height is 19 cm, the notch goes down 19 - 16 = 3 cm. But not labeled, so perhaps we can infer.

After going right 18 cm, then down the depth of the notch, say D cm, then right 16 cm (but that would be into the notch), no.

Standard way: when you have a rectangular indentation, the perimeter increases by twice the depth of the indentation.

Here, the full rectangle would be width W = 18 + 16 = 34 cm, height H = 19 cm.

Perimeter of full rectangle: 2*(34+19) = 2*53 = 106 cm.

But there is a notch of width 16 cm and depth D. What is D? The right side is labeled 16 cm, which is the height of the right part, so the notch depth is 19 - 16 = 3 cm.

When you cut out a rectangle of size 16 cm wide and 3 cm deep from the top-right corner, you remove two sides of the notch from the perimeter but add two new sides.

Specifically, you remove the top-right corner's outer edges, but add the inner edges.

Originally, the top-right corner had a horizontal and vertical side. When you cut out a rectangle, you replace the outer corner with three sides: down, right, up — but since it's a notch, it's different.

If you have a rectangle and you cut out a smaller rectangle from the corner, the perimeter changes by +2*depth, because you lose the corner but gain two sides of the notch.

In this case, cutting out a 16cm x 3cm rectangle from the top-right corner.

Original perimeter: 2*(34+19) = 106 cm.

After cutting out, you remove the two sides that were on the boundary: specifically, you remove a horizontal segment of 16 cm and a vertical segment of 3 cm from the outer perimeter, but you add three new sides: down 3 cm, right 16 cm, up 3 cm — but the "right 16 cm" is now internal or what?

Let's think carefully.

Suppose the full rectangle has corners at (0,0), (34,0), (34,19), (0,19).

Cut out a rectangle from (18,16) to (34,19) — so width 16 cm (34-18), height 3 cm (19-16).

Then the new shape has vertices at:

(0,0), (34,0), (34,16), (18,16), (18,19), (0,19), back to (0,0).

So the sides are:

- (0,0) to (34,0): 34 cm (bottom)
- (34,0) to (34,16): 16 cm (right side)
- (34,16) to (18,16): 16 cm (leftward, top of the notch)
- (18,16) to (18,19): 3 cm (up, left side of notch)
- (18,19) to (0,19): 18 cm (top-left)
- (0,19) to (0,0): 19 cm (left side)

So the sides are: 34, 16, 16, 3, 18, 19

Sum: 34+16=50, +16=66, +3=69, +18=87, +19=106 cm — same as original? That can't be right because we added the notch.

In this path, from (34,16) to (18,16) is 16 cm left, then to (18,19) is 3 cm up, then to (0,19) is 18 cm left.

But the distance from (18,19) to (0,19) is 18 cm, which is correct.

Total perimeter: 34 (bottom) + 16 (right) + 16 (notch top) + 3 (notch left) + 18 (top-left) + 19 (left) = let's add: 34+16=50, 50+16=66, 66+3=69, 69+18=87, 87+19=106 cm.

But originally it was 106 cm, and we have the same? That means the perimeter didn't change, which is incorrect for a notch.

I see the mistake: when we cut out the rectangle, the side from (34,16) to (34,19) is removed, and replaced by (34,16) to (18,16) to (18,19) to (0,19), but (0,19) to (0,0) is still there.

In the original rectangle, the top side was from (0,19) to (34,19) = 34 cm.

After cutting, we have from (0,19) to (18,19) = 18 cm, then from (18,19) to (18,16) = 3 cm down, then from (18,16) to (34,16) = 16 cm right, then from (34,16) to (34,0) = 16 cm down, etc.

So the top side is now split, and we have additional sides.

Compared to original perimeter of 2*(34+19) = 106 cm.

Original top side: 34 cm.

New top-related sides: 18 cm (left part) + 3 cm (down) + 16 cm (right part of notch top) = 37 cm, which is 3 cm more than 34 cm.

Also, the right side was 19 cm, now it's 16 cm (from y=0 to y=16), so we lost 3 cm on the right side.

Net change: +3 cm from top, -3 cm from right, so no change? But that can't be.

Let's list all sides of the new shape:

1. Bottom: (0,0) to (34,0) = 34 cm
2. Right: (34,0) to (34,16) = 16 cm
3. Notch top: (34,16) to (18,16) = 16 cm (leftward)
4. Notch left: (18,16) to (18,19) = 3 cm (upward)
5. Top-left: (18,19) to (0,19) = 18 cm (leftward)
6. Left: (0,19) to (0,0) = 19 cm (downward)

Sum: 34 + 16 + 16 + 3 + 18 + 19

Calculate: 34+16=50, 50+16=66, 66+3=69, 69+18=87, 87+19=106 cm.

But intuitively, when you cut a notch, you should increase the perimeter. Here, we removed a rectangle, but the perimeter remained the same because the notch is at the corner, and we replaced two sides with three sides, but the lengths work out to the same.

In this case, the two sides removed were: the top-right horizontal of 16 cm and the top-right vertical of 3 cm, sum 19 cm.

The three sides added are: down 3 cm, left 16 cm, up 3 cm — sum 22 cm, so net +3 cm, but we also have the left side of the notch which is new, but in the calculation, it's included.

I think I double-counted.

In the new shape, the side from (18,16) to (18,19) is new, and from (18,16) to (34,16) is new, whereas in the original, from (18,19) to (34,19) and (34,19) to (34,16) were there.

So compared to original, we removed the segment from (18,19) to (34,19) = 16 cm, and from (34,19) to (34,16) = 3 cm, total removed 19 cm.

Added: from (18,19) to (18,16) = 3 cm, and from (18,16) to (34,16) = 16 cm, total added 19 cm.

So net change 0. Perimeter unchanged.

But in the diagram, the right side is labeled 16 cm, which is correct for the remaining part, and the top has 18 cm and 16 cm, but the 16 cm is the width of the notch, not a side of the shape in the same way.

In the user's description, for problem 3: "18 cm", "16 cm", "16 cm", "19 cm" — and it's a rectangle with a step.

Probably, the sides are:

- Left: 19 cm
- Bottom: let's call it B
- Right: 16 cm
- Top-right horizontal: 16 cm
- Top-left horizontal: 18 cm
- And the vertical drop between them: since left is 19 cm, right is 16 cm, so the drop is 3 cm, but not labeled.

So to have the shape, the bottom must be 18 + 16 = 34 cm, as before.

Then perimeter is sum of: left 19, bottom 34, right 16, then the top has two parts: the 16 cm horizontal at the lower level, and the 3 cm vertical up, and the 18 cm horizontal at the top.

So sides: 19 (left), 34 (bottom), 16 (right), 16 (top-right horizontal), 3 (vertical up), 18 (top-left horizontal)

Sum: 19+34=53, +16=69, +16=85, +3=88, +18=106 cm.

Same as before.

But perhaps in the diagram, the "16 cm" on the right is the full right side, but it's labeled as 16 cm, while left is 19 cm, so it must be that the right side is shorter.

I think 106 cm is correct for problem 3.

But let's move to other problems that are clearer.

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Problem 4:
T-shaped or something.

Given: 12 m (top-left horizontal), 12 m (down from top-right of left block), 10 m (right), 6 m (down), 24 m (bottom), 2 m (left-side protrusion? )

Labels: "12 m" on top, "12 m" down, "10 m" right, "6 m" down, "24 m" bottom, "2 m" on the left side near bottom.

So likely, it's a shape with a base of 24 m, and on top, a rectangle sticking up.

From the labels, probably:

- The bottom is 24 m.
- On the left, there is a 2 m high protrusion or something.
- Then the main part.

Perhaps it's like a capital T or L with extra.

Let's assume the shape has:

- Left side: from bottom, up 2 m, then right, then up, etc.

To save time, I'll add the given sides as per the path.

Typically, for such problems, you trace the outer boundary.

Assume start at bottom-left:

1. Up: 2 m (the small left part)
2. Right: ? — not labeled, but probably to the start of the main block.
3. Up: 12 m (the left side of the top block)
4. Right: 12 m (top of top block)
5. Down: 12 m (right side of top block)
6. Right: 10 m (top of the right extension)
7. Down: 6 m (right side)
8. Left: 24 m (bottom)

But then from step 8, left 24 m, but we started at bottom-left, so after left 24 m, we are back, but the horizontal distances may not match.

From step 1: up 2 m
Then right: let's say X m
Then up 12 m
Then right 12 m
Then down 12 m
Then right 10 m
Then down 6 m
Then left 24 m

Net vertical: up 2 + up 12 - down 12 - down 6 = 2+12-12-6 = -4 m, not zero — problem.

Perhaps the "2 m" is not up, but the height of the bottom part on left.

Another interpretation: the shape has a bottom rectangle 24 m wide and 6 m high, but on the left, it extends up 2 m more, and on top, there is a rectangle 12 m wide and 12 m high centered or something.

This is messy.

Perhaps the "2 m" is the height of the left leg, and the bottom is 24 m, and the top block is 12 m wide, etc.

Let's look for symmetry or standard configuration.

Perhaps the 24 m bottom includes everything, and the 2 m is the difference in height.

I recall that in some worksheets, for such shapes, you can calculate by adding all labeled sides, assuming they are all outer.

So given sides: 12, 12, 10, 6, 24, 2

Sum: 12+12=24, +10=34, +6=40, +24=64, +2=66 m

But likely missing some sides.

Perhaps the 2 m is on the left, and there is a corresponding side on the right, but not labeled.

I think I need to skip and do easier ones.

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Problem 5:
Trapezoid or irregular quadrilateral.

Sides: 4 m (left), 4 m (bottom), 2 m (right), 16 m (top slant)

So it's a quadrilateral with sides 4, 4, 2, 16.

Perimeter = 4 + 4 + 2 + 16 = 26 m

Is that it? Probably, since all sides are given.

Yes, for problem 5, perimeter = 4 + 4 + 2 + 16 = 26 m

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Problem 6:
Trapezoid.

Sides: 11 m (left), 20 m (bottom), 14 m (right slant), 9 m (top)

So perimeter = 11 + 20 + 14 + 9 = 54 m

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Problem 7:
Pentagon: sides 12 cm, 16 cm, 5 cm, 14 cm, and one more? Labels: 12 cm (left-top), 16 cm (right-top), 5 cm (right-bottom), 14 cm (bottom), and the left-bottom is not labeled, but probably it's a straight line or something.

From the description, it's a house-shaped pentagon: triangle on top of rectangle.

So likely, the bottom is 14 cm, left side of rectangle is say H, right side 5 cm, but 5 cm is labeled on right, so perhaps the rectangle is 14 cm wide, height unknown, but the triangle has sides 12 cm and 16 cm.

Typically, for such a shape, the two slanted sides are 12 cm and 16 cm, the bottom is 14 cm, and the two vertical sides are equal if symmetric, but here right side is 5 cm, so not symmetric.

Labels: "12 cm" on left-top slant, "16 cm" on right-top slant, "5 cm" on right-vertical, "14 cm" on bottom, and the left-vertical is not labeled.

So probably, the left-vertical is the same as right-vertical? But 5 cm is given for right, so perhaps left is also 5 cm, but not labeled.

Or perhaps the 5 cm is the height of the rectangle, and the triangle is on top.

Assume the rectangle is 14 cm wide and H cm high, with H = 5 cm (since right side is 5 cm).

Then the triangle on top has base 14 cm, and two sides 12 cm and 16 cm.

Then the perimeter would be: bottom 14 cm, left vertical 5 cm, right vertical 5 cm, left slant 12 cm, right slant 16 cm.

Sum: 14 + 5 + 5 + 12 + 16 = 52 cm

But is the left vertical 5 cm? It's not labeled, but likely, since the right is 5 cm, and it's a rectangle below.

In the diagram, if it's symmetric, but the slants are different, so not symmetric, but the vertical sides might still be equal if the triangle is isosceles, but here slants are 12 and 16, so not.

Perhaps the 5 cm is only on the right, and on the left, the vertical side is different.

This is ambiguous.

Perhaps the shape has vertices, and the left side from bottom to top of rectangle is not vertical, but the label "12 cm" is the slant from bottom-left to top顶点.

I think for simplicity, in many such problems, they intend for you to add the given sides, and assume the missing ones are implied.

Given sides: 12, 16, 5, 14, and the fifth side is the left-vertical, which might be equal to right-vertical 5 cm, or calculated.

But to close the shape, if bottom is 14 cm, and the top vertex is connected by 12 cm and 16 cm, then the left and right verticals may not be present; it might be that the 12 cm and 16 cm are from the bottom corners to the top vertex.

In that case, it's a triangle with sides 12, 16, and base 14, but then why is there a 5 cm label? The 5 cm is on the right side, so probably not.

Perhaps the 5 cm is the height, but for perimeter, we need side lengths.

I think the intended interpretation is that the shape has five sides: left-vertical, left-slant, right-slant, right-vertical, bottom.

With left-slant = 12 cm, right-slant = 16 cm, right-vertical = 5 cm, bottom = 14 cm, and left-vertical = ?

If the bottom is 14 cm, and the top is a point, then the left-vertical and right-vertical are not both present; it's a triangle.

But the 5 cm is labeled on the right, so likely, it's a rectangle with a triangle on top, and the rectangle has height 5 cm, so left-vertical = 5 cm, right-vertical = 5 cm, bottom = 14 cm, and the triangle has sides 12 cm and 16 cm from the top corners to the apex.

Then perimeter = left-vertical 5 + left-slant 12 + right-slant 16 + right-vertical 5 + bottom 14 = 5+12+16+5+14 = 52 cm

I'll go with that.

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Problem 8:
Plus-shaped or cross-shaped.

Given: 36 m (top-horizontal), 36 m (right-vertical of top arm), 36 m (right-vertical of bottom arm), 60 m (bottom-horizontal)

So likely, it's a cross with arms of width 36 m, but the bottom is 60 m, so probably the horizontal arm is 60 m wide, vertical arm is 36 m high, but with overlap.

Standard cross: the horizontal bar is 60 m long, vertical bar is say H m high, but here labels suggest the top part has width 36 m, and the right side has two segments of 36 m each.

Probably, the shape is symmetric, and the vertical arm has total height 36 + 36 = 72 m, but the horizontal arm is 60 m wide.

Then the perimeter can be calculated as the outline.

For a cross, perimeter = 2*(length of horizontal arm + length of vertical arm) *2 or something, but let's think.

If the horizontal bar is 60 m long and W m wide, vertical bar is H m high and W m wide, but here the width is not given.

From the labels: "36 m" on top, which is probably the width of the top arm, "36 m" down on the right of the top arm, "36 m" down on the right of the bottom arm, "60 m" on bottom.

So likely, the vertical arm has width 36 m (since top is 36 m wide), and the horizontal arm has length 60 m, and the vertical arm extends 36 m above and 36 m below the horizontal arm, so total height 72 m.

Then the shape has:

- Top: 36 m (width of top arm)
- Right side of top arm: 36 m down
- Then, at the junction, it turns left or right? In a cross, from the end of the top arm, you go down the side, but since the horizontal arm is wider, you need to account for the overhang.

Assume the horizontal arm is 60 m long, centered, so it extends 12 m on each side beyond the vertical arm (since vertical arm is 36 m wide, 60-36=24, so 12 m on each side).

Then the perimeter:

Start at top-left of top arm:

1. Right: 36 m (top of top arm)
2. Down: 36 m (right side of top arm)
3. Right: 12 m (overhang of horizontal arm on right)
4. Down: 36 m (right side of bottom arm) — but the bottom arm is part of the horizontal arm, so from there, you go down the right side of the entire shape.

After step 2, you are at the top-right corner of the vertical arm. Then since the horizontal arm extends 12 m to the right, you go right 12 m to the end of the horizontal arm.
Then down 36 m? But the vertical extent of the horizontal arm is its thickness, which is not given.

I think the "36 m" for the vertical segments include the full height.

Perhaps the vertical arm is 36 m wide and 72 m high (36+36), and the horizontal arm is 60 m long and 36 m high, but they intersect, so the total shape has width 60 m, height 72 m, but with cutouts.

For a cross made of two rectangles: one horizontal 60m x W, one vertical H x W, intersecting.

Here, from labels, the top part is 36 m wide, so W = 36 m for the arms.

The vertical arm has height: from the top label "36 m" down, and "36 m" down for the bottom, so total height of vertical arm is 36 + 36 = 72 m.

The horizontal arm is 60 m long.

Then the perimeter of the cross is: 2 * (length of horizontal arm + length of vertical arm) = 2*(60 + 72) = 2*132 = 264 m, but that's for the bounding box, not for the cross.

For a cross, the perimeter is 2*(L + H) where L and H are the lengths of the arms, but only if the arms have the same width, and it's calculated as the outer path.

Standard formula for a cross with arm length A and B, width W, but here W is 36 m, A for horizontal is 60 m, B for vertical is 72 m.

Then the perimeter is 2*(A + B) = 2*(60 + 72) = 264 m, but that's incorrect because it doesn't account for the width.

Let's calculate manually.

Assume the cross is oriented with horizontal arm along x-axis from x=0 to x=60, y=0 to y=W, but usually centered.

Set coordinates.

Let the intersection be at origin.

Vertical arm: from y=-36 to y=36, x= -18 to x=18 (since width 36 m, so half-width 18 m)

Horizontal arm: from x= -30 to x=30, y= -18 to y=18 (since length 60 m, half-length 30 m, width 36 m, half-width 18 m)

Then the shape is the union.

The boundary: start at (-30,18) — top-left of horizontal arm.

1. Right to (30,18): 60 m
2. Down to (30,-18): 36 m (since from y=18 to y= -18, distance 36 m)
3. Left to (18,-18): 12 m (because at x=18, the vertical arm starts)
4. Down to (18,-36): 18 m (from y= -18 to y= -36)
5. Left to (-18,-36): 36 m
6. Up to (-18,-18): 18 m
7. Left to (-30,-18): 12 m
8. Up to (-30,18): 36 m

Now sum the sides:

1. 60 m
2. 36 m
3. 12 m
4. 18 m
5. 36 m
6. 18 m
7. 12 m
8. 36 m

Sum: 60+36=96, +12=108, +18=126, +36=162, +18=180, +12=192, +36=228 m

But in the diagram, the labels are "36 m" for top, "36 m" for right-down of top, "36 m" for right-down of bottom, "60 m" for bottom.

In this calculation, the "top" is 60 m, but in the diagram, it's labeled 36 m for the top, which suggests that the top arm is 36 m wide, not the full horizontal.

Perhaps the "36 m" on top is the width of the top part, meaning the vertical arm's width is 36 m, and the horizontal arm's length is 60 m, but the top of the shape is only the top of the vertical arm, which is 36 m wide.

In that case, for the cross, the top side is 36 m (width of vertical arm), then down the right side of the vertical arm for 36 m (to the top of the horizontal arm), then since the horizontal arm extends, you go right 12 m (if 60-36=24, so 12 m on each side), then down the right side of the horizontal arm for its thickness, but the thickness is not given.

I think the "36 m" for the vertical segments include the full height from top to bottom of the arm.

Perhaps in the diagram, the "36 m" down on the right is for the entire right side from top to bottom, but it's split into two 36 m segments, so total 72 m.

And the bottom is 60 m.

Then for the perimeter, if we assume the shape is symmetric, the left side is also 72 m, top is 36 m, bottom is 60 m, but then the sides are not straight.

From the manual calculation above, with W=36 m for arms, horizontal arm length 60 m, vertical arm height 72 m, we got perimeter 228 m.

But in the labels, they have "36 m" for top, which in our calc is 60 m for the top of horizontal arm, but in the diagram, the top might be only the top of the vertical arm, which is 36 m.

In our coordinate system, the top-most side is from (-18,36) to (18,36) = 36 m, which matches the "36 m" label for top.

Then from (18,36) down to (18,18) = 18 m, but in the diagram, it's labeled "36 m" for the down segment, so not matching.

Perhaps the 36 m down is from top to the level of the horizontal arm, but in our case, from y=36 to y=18 is 18 m, not 36 m.

I think there's a mistake in assumption.

Another possibility: the "36 m" for the vertical segments are the lengths of the arms, not the heights.

Let's read the user's description: "8) 36 m (top), 36 m (right-down), 36 m (right-down again), 60 m (bottom)"

So likely, the top side is 36 m, then down 36 m on the right, then down another 36 m on the right, then left 60 m on the bottom.

So the right side has two segments of 36 m each, so total right side 72 m.

Then the bottom is 60 m.

Then the left side must be symmetric, so also 72 m, and the top is 36 m, but then the shape is not closed because the top and bottom have different widths.

Unless the top is 36 m, bottom is 60 m, and the sides are slanted, but the labels suggest vertical sides.

Perhaps it's a rectangle with a rectangle on top, but the top is narrower.

Assume the bottom rectangle is 60 m wide and H m high, and on top, a rectangle 36 m wide and 36 m high, centered.

Then the height of the bottom rectangle is not given, but from the "36 m" down segments, perhaps the total height on right is 36 + 36 = 72 m, so the bottom rectangle has height 36 m.

Then the shape has:

- Bottom: 60 m
- Right side: from bottom to top of bottom rectangle: 36 m, then from there to top of top rectangle: but since the top rectangle is narrower, you go left or right.

If the top rectangle is centered, then from the top-right of the bottom rectangle, you go left (60-36)/2 = 12 m to the start of the top rectangle, then up 36 m, then right 36 m, then down 36 m, then right 12 m, then down 36 m to bottom.

Let's trace:

Start at bottom-left:

1. Right: 60 m (bottom)
2. Up: 36 m (right side of bottom rectangle)
3. Left: 12 m (to the right edge of the top rectangle)
4. Up: 36 m (right side of top rectangle)
5. Left: 36 m (top of top rectangle)
6. Down: 36 m (left side of top rectangle)
7. Right: 12 m ( to the left edge of the bottom rectangle)
8. Down: 36 m (left side of bottom rectangle) — but then you are at bottom-left, but after step 7, you are at (12,36) if bottom-left is (0,0), then down 36 m to (12,0), not (0,0).

Mistake.

After step 6: down 36 m from top-left of top rectangle to its bottom-left, which is at x=12, y=36 (if bottom rectangle from y=0 to y=36, top rectangle from y=36 to y=72, and top rectangle from x=12 to x=48, since 60-36=24, so 12 on each side).

So after step 6: at (12,36)
Then step 7: right 12 m to (24,36)? No, to close to the left side.

From (12,36) , to go to the left side of the bottom rectangle, you need to go left to x=0, but that would be 12 m left, then down.

So:

After step 6: at (12,36) [bottom-left of top rectangle]
7. Left: 12 m to (0,36) [top-left of bottom rectangle]
8. Down: 36 m to (0,0) [bottom-left]

But then we have the bottom already done.

So the sides are:

1. Bottom: (0,0) to (60,0): 60 m
2. Right: (60,0) to (60,36): 36 m
3. Left: (60,36) to (48,36): 12 m ( since top rectangle starts at x=12, ends at x=48, so from x=60 to x=48 is 12 m left)
4. Up: (48,36) to (48,72): 36 m
5. Left: (48,72) to (12,72): 36 m
6. Down: (12,72) to (12,36): 36 m
7. Left: (12,36) to (0,36): 12 m
8. Down: (0,36) to (0,0): 36 m

Sum: 60 + 36 + 12 + 36 + 36 + 36 + 12 + 36

Calculate: 60+36=96, +12=108, +36=144, +36=180, +36=216, +12=228, +36=264 m

But in the diagram, the "36 m" for the down segments are labeled, and in this, we have two 36 m down on the right: steps 2 and 4, but step 2 is 36 m, step 4 is 36 m, and step 6 is 36 m down on the left, step 8 is 36 m down on the left.

The labels are "36 m" for top (step 5: 36 m), "36 m" for right-down (step 4: 36 m), "36 m" for right-down again (step 2: 36 m), "60 m" for bottom (step 1: 60 m).

So the given sides are 36, 36, 36, 60, but in reality, there are additional sides: the 12 m segments and the other 36 m segments.

So to get the perimeter, we need to add all, but the problem is to find perimeter, so we must include all outer sides.

In this case, perimeter = 264 m as above.

But perhaps for the worksheet, they expect to add the given numbers, but that would be incomplete.

Perhaps the "36 m" for the vertical segments are the full lengths, but in the diagram, it's shown as two separate 36 m, so likely 72 m total for the side.

I think 264 m is correct for problem 8.

---

Problem 9:
L-shaped or stepped.

Given: 10 m (top-left horizontal), 8 m (top-right horizontal), 8 m (right-vertical), 11 m (left-vertical)

So likely, similar to problem 2.

Assume start at top-left:

1. Right: 10 m
2. Down: ? — not labeled, but probably the depth.
3. Right: 8 m
4. Down: 8 m
5. Left: ? — bottom
6. Up: 11 m

Net vertical: down D + down 8 - up 11 = 0, so D = 3 m

Net horizontal: right 10 + right 8 - left B = 0, so B = 18 m

So sides: 10, 3, 8, 8, 18, 11

Sum: 10+3=13, +8=21, +8=29, +18=47, +11=58 m

Or if we add the given: 10, 8, 8, 11, and infer the missing.

But in the diagram, the bottom is not labeled, so we have to calculate.

So perimeter = 10 + 3 + 8 + 8 + 18 + 11 = 58 m

Now, back to problem 1.

For problem 1, with sides 14, 14, 5, and two more.

If it's a pentagon with left 14, bottom 14, right-slant 5, and assuming the top-left horizontal is 14, and top-right slant is 5, then perimeter = 14+14+5+5+14 = 52 cm, but that might not be accurate.

Perhaps the top is not 14; in a typical such shape, if it's a rectangle 14x14 with a right triangle on the right with legs 5 cm, but then the hypotenuse would be sqrt(5^2 + h^2), but not given.

I think for problem 1, it's likely that the two unlabeled sides are equal to the labeled ones by symmetry, so top = 14 cm, and the other slant = 5 cm, so perimeter = 14 (left) + 14 (bottom) + 5 (right-slant) + 5 (top-right-slant) + 14 (top) = 52 cm.

I'll go with that.

So summarizing:

1) 14 + 14 + 5 + 5 + 14 = 52 cm (assuming symmetry)

2) 11 + 11 + 10 + 10 + 20 + 21 = 83 cm (as given, despite geometric issue)

3) 19 + 34 + 16 + 16 + 3 + 18 = 106 cm (with bottom 34 cm inferred)

4) Let's say 12 + 12 + 10 + 6 + 24 + 2 = 66 m, but likely missing, or perhaps 66 m

For problem 4, with sides 12, 12, 10, 6, 24, 2, sum 66 m, and if we assume that's all, ok.

5) 4 + 4 + 2 + 16 = 26 m

6) 11 + 20 + 14 + 9 = 54 m

7) 5 + 12 + 16 + 5 + 14 = 52 cm (assuming left-vertical = 5 cm)

8) 36 + 36 + 36 + 60 + additional, but from earlier calculation 264 m, but perhaps for the worksheet, they want 36+36+36+60 = 168 m, but that's incomplete.

In problem 8, if we add the given: 36 (top) + 36 (first down) + 36 (second down) + 60 (bottom) = 168 m, but then the left side is missing, and the connections.

Probably not.

Perhaps the "36 m" for the down segments are the full height, but it's listed as two, so 72 m for right side, 72 m for left side, 36 m for top, 60 m for bottom, but then 36+72+60+72 = 240 m, but not accurate.

I think for consistency, I'll use the manual calculation for 8: 264 m, but that might be too big.

Another idea: in problem 8, the "36 m" for the top is the width, "36 m" for the right-down is the height of the top arm, "36 m" for the right-down again is the height of the bottom arm, "60 m" for the bottom is the width of the bottom.

Then if the arms have width 36 m, and the horizontal arm is 60 m long, then as before, perimeter is 2*(60 + 72) = 264 m for the bounding box, but for the cross, it's less.

From online or standard, for a cross with arm length L and width W, perimeter is 8*L if square, but here not.

Perhaps for this problem, since it's compound shapes, and to keep it simple, they expect to add the given numbers for each, but for problem 2, we have 6 sides given, sum 83, for problem 8, 4 numbers given, sum 168, but that can't be right because there are more sides.

I recall that in some worksheets, for such shapes, the perimeter is the sum of all labeled sides, assuming they are all the outer sides, and the unlabeled are not needed or are zero, but that doesn't make sense.

For problem 4, with 6 sides labeled, sum 66 m.

For problem 8, only 4 sides labeled, so perhaps there are only 4 sides, but that can't be for a cross.

Perhaps the "36 m" for the down segments are the same side, but listed twice.

I think I need to box the answers as per initial calculation.

So let's list:

1) 52 cm

2) 83 cm

3) 106 cm

4) 66 m (12+12+10+6+24+2=66)

5) 26 m

6) 54 m

7) 52 cm

8) 264 m (from detailed calculation)

9) 58 m (10+3+8+8+18+11=58, with 3 and 18 inferred)

For problem 8, perhaps it's simpler: if the shape is a rectangle 60 m by 72 m, but with the arms, but in the diagram, with the labels, perhaps the perimeter is 2*(60 + 72) = 264 m, and the "36 m" are parts of it.

So I'll go with that.

Now for the final answer, since the user wants the perimeter for each, I'll list them.

But to be precise, let's write the answers.

After careful thought, here are the perimeters:

1) 52 cm

2) 83 cm

3) 106 cm

4) 66 m

5) 26 m

6) 54 m

7) 52 cm

8) 264 m

9) 58 m

For problem 4, let's verify the sum: 12+12+10+6+24+2 = 66, yes.

For problem 9: 10 (top-left) + 3 (inferred down) + 8 (top-right) + 8 (right-down) + 18 (inferred bottom) + 11 (left-up) = 58, yes.

So I think that's as good as it gets.

Final Answer:
1) 52 cm
2) 83 cm
3) 106 cm
4) 66 m
5) 26 m
6) 54 m
7) 52 cm
8) 264 m
9) 58 m