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

Let’s solve each problem one by one. Remember, perimeter means adding up all the outer sides of the shape.

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1)
Sides: 14 cm, 14 cm, 5 cm, and two slanted sides that are equal to the other sides (since it’s symmetric). Wait — actually, looking at the shape, it’s a rectangle with a triangle on the right. But we’re only given three side lengths: left = 14 cm, bottom = 14 cm, top-right slant = 5 cm. The top-left is same as bottom? Actually, no — let’s look again.

Actually, this shape has:
- Left vertical: 14 cm
- Bottom horizontal: 14 cm
- Right slant: 5 cm
- Top slant: also 5 cm? No — wait, the top is not labeled. Hmm.

Wait — maybe it’s a pentagon? Let me count the sides:

It has 5 sides:
- Left: 14 cm
- Bottom: 14 cm
- Right diagonal: 5 cm
- Top diagonal: must be same as right? Not necessarily.

Actually, looking carefully — the top edge is missing a label. But in many such problems, if it looks like a rectangle with a triangle attached, sometimes the top and bottom are equal. But here, bottom is 14 cm, left is 14 cm, and the two slants are both 5 cm? That doesn’t add up.

Wait — perhaps I misread. Let me re-express:

Shape 1: It’s a house-like shape but tilted? Actually, no — it’s a rectangle with a triangular point on the right. So:

Left side: 14 cm
Bottom: 14 cm
Top: should also be 14 cm? But it’s not drawn straight — it goes diagonally up then down? No.

Actually, looking at the diagram again (mentally), it’s a quadrilateral? No — five sides.

List all visible labeled sides:

- Left vertical: 14 cm
- Bottom horizontal: 14 cm
- Right upper slant: 5 cm
- And there’s another slant on the top right? Actually, the figure shows two slanted sides meeting at a point on the right.

So total sides:

1. Left: 14 cm
2. Bottom: 14 cm
3. Right lower slant: ?
4. Right upper slant: 5 cm
5. Top: ?

This is confusing without seeing exact labels. But in standard worksheets, for shape 1, often the top is same as bottom, and the two slants are equal. But here only one slant is labeled 5 cm.

Wait — perhaps the top edge is not labeled because it’s equal to the bottom? Or maybe it’s implied.

Alternatively, maybe the shape is made so that the top horizontal part is missing, and instead there are two diagonals.

But let’s think differently — perhaps the figure is symmetric. If left is 14, bottom is 14, and the right has two sides of 5 cm each? Then what about the top?

Actually, I recall that in some versions of this worksheet, shape 1 has:

- Left: 14 cm
- Bottom: 14 cm
- Two slanted sides on right: each 5 cm
- And the top is also 14 cm? But that would make it a hexagon? No.

Wait — let's count the vertices. From left-bottom, go right 14 cm, then up-diagonal 5 cm, then left-diagonal 5 cm, then down 14 cm? That doesn't close.

I think I need to assume based on common problems.

Upon second thought — in many "compound shapes" worksheets, shape 1 is a rectangle with a triangle on the end, but here it's drawn as a pentagon with sides: 14, 14, 5, and two more.

Perhaps the top side is not labeled because it's equal to the bottom? But that doesn't help.

Another idea: maybe the two slanted sides are both 5 cm, and the top is the same as the bottom, 14 cm. Then perimeter = 14 + 14 + 5 + 5 + 14? That's 52, but that seems too big.

Wait — let's look at the actual standard answer for this type of problem.

I remember now: for shape 1, it's often a shape where you have:

- Vertical left: 14 cm
- Horizontal bottom: 14 cm
- Then a diagonal up-right: 5 cm
- Then a diagonal down-right: but that doesn't make sense.

Perhaps it's a trapezoid or something else.

Let me try to sketch mentally:

Start at bottom-left corner. Go right 14 cm (bottom). Then go up-right at an angle for 5 cm to the tip. Then from tip, go left-down at an angle back to the top-left? But top-left is connected to bottom-left by 14 cm vertical.

So the sides are:

1. Bottom: 14 cm
2. Right-lower slant: 5 cm
3. Right-upper slant: ? — not labeled
4. Top: ? — not labeled
5. Left: 14 cm

This is problematic. Perhaps in the original image, the top side is labeled or implied.

Wait — looking back at the user's description, for shape 1, it says: "14 cm" on left, "14 cm" on bottom, "5 cm" on the right slant. And the top is not labeled, but in many such diagrams, the top is parallel to bottom and same length, but here it's not straight.

Another possibility: the shape is a rectangle 14x14 with a right triangle attached on the right, but the hypotenuse is 5 cm? That can't be because if legs are say a and b, hypotenuse 5, but then the total width would be 14 + a, etc.

I think I found the issue — in the actual worksheet, for shape 1, the two slanted sides are both 5 cm, and the top is 14 cm, but that would mean the shape has six sides? No.

Let's count the edges in the drawing: typically, it's a pentagon with sides: left vertical, bottom horizontal, right-lower diagonal, right-upper diagonal, and top horizontal. But top horizontal is not labeled.

Perhaps the top horizontal is equal to the bottom minus something, but no values given.

I recall that in some versions, the top is not needed because the two diagonals replace the right side, but still.

Let's calculate based on common knowledge: for shape 1, perimeter is usually 14 + 14 + 5 + 5 + 14 = 52 cm? But that assumes top is 14, which may not be correct.

Perhaps the top is the same as the bottom, 14 cm, and the two slants are 5 cm each, and left is 14 cm, so total 14+14+5+5+14=52 cm.

But let's move to other shapes and come back.

2) L-shape.

Given:
- Left vertical: 21 cm
- Bottom horizontal: 20 cm
- Top-left horizontal: 11 cm
- Right-vertical part: 10 cm
- Inner horizontal: 10 cm
- Inner vertical: 11 cm

To find perimeter, we add all outer sides.

The outer path: start from bottom-left, go right 20 cm, up 10 cm, left 10 cm, up 11 cm, left 11 cm, down 21 cm.

Let's list the outer sides:

- Bottom: 20 cm
- Right-bottom vertical: 10 cm
- Middle horizontal (leftward): 10 cm
- Right-top vertical: 11 cm
- Top horizontal: 11 cm
- Left vertical: 21 cm

Sum: 20 + 10 + 10 + 11 + 11 + 21 = let's calculate: 20+10=30, +10=40, +11=51, +11=62, +21=83 cm.

Is that correct? Let me verify.

Another way: the full rectangle would be 21 cm high and 20 cm wide, but with a bite taken out. The bite is 11 cm wide and 11 cm high? From the labels, the cut-out is 10 cm wide and 11 cm high? Let's see.

From the top, the top arm is 11 cm wide, and the right arm is 10 cm high, and the inner corner has 10 cm horizontal and 11 cm vertical.

The perimeter should be the same as the outer rectangle if no cut, but with cut, we add the inner sides.

Standard way: for L-shape, perimeter = 2*(length + width) if it were rectangle, but here it's not.

Better to trace the boundary.

Start at bottom-left corner:

- Move right along bottom: 20 cm
- Move up along right side: but only 10 cm (since above that is indented)
- Move left along the indent: 10 cm (this is the inner horizontal)
- Move up along the inner vertical: 11 cm
- Move left along the top: 11 cm
- Move down along left side: 21 cm back to start.

Yes, so sides are: 20, 10, 10, 11, 11, 21.

Sum: 20+10=30; 30+10=40; 40+11=51; 51+11=62; 62+21=83 cm.

Okay, so for 2) perimeter is 83 cm.

3) Another L-shape.

Labels:
- Left vertical: 19 cm
- Bottom horizontal: ? not directly given, but from context.
- Top-left horizontal: 18 cm
- Right-vertical part: 16 cm
- Inner horizontal: 16 cm
- Inner vertical: ?

From the diagram, the total height is 19 cm, the right part is 16 cm high, so the inner vertical drop is 19 - 16 = 3 cm? But not labeled.

Similarly, the bottom width: the top arm is 18 cm, and the right arm extends further, but how much?

The inner horizontal is labeled 16 cm, which is the width of the right part.

So, the total width = top arm width + right arm width? No.

Typically, for such L-shape, the bottom width is the sum of the top horizontal and the inner horizontal? Let's think.

From left to right: the top part is 18 cm wide, then below it, the right part sticks out, and its width is given by the inner horizontal label, which is 16 cm. But that 16 cm is the length of the horizontal segment inside, which corresponds to the width of the right leg.

So, the total width of the shape is 18 cm (top) + 16 cm (right extension)? But that might not be accurate.

Better to trace the perimeter.

Start at bottom-left:

- Move right along bottom: this should be the total width. What is it? From the labels, the left part has width corresponding to the top 18 cm, but the bottom extends further.

Actually, the bottom width is not labeled, but we can infer.

The vertical sides: left is 19 cm, right is 16 cm, so the difference is 3 cm, which is the height of the "step".

Horizontally, the top is 18 cm, and the inner horizontal is 16 cm, which is the width of the right leg.

So, the total width = width of left part + width of right part = 18 cm + 16 cm = 34 cm? But is that correct?

Let's see the path:

Start at bottom-left corner.

- Move right along bottom: distance = ? Let's call it W.
- Move up along right side: 16 cm (given)
- Move left along the top of the right leg: 16 cm (inner horizontal label)
- Move up along the inner vertical: this should be 19 - 16 = 3 cm (since total height 19, right part 16)
- Move left along the top: 18 cm
- Move down along left side: 19 cm

But when we move left along the top, it's 18 cm, and then down 19 cm, but we started at bottom-left, so after moving down 19 cm, we are back.

Now, the bottom width W should be equal to the top width plus the overhang? In this case, the top is 18 cm, and the right leg extends beyond by the amount of the inner horizontal, which is 16 cm, but that doesn't make sense because 18 + 16 = 34, but the right leg's width is 16 cm, and it's attached to the right of the top part, so yes, total width is 18 + 16 = 34 cm.

Confirm with the vertical: the left side is 19 cm, the right side is 16 cm, and the step up is 3 cm, which matches 19-16=3.

So perimeter sides:

- Bottom: 34 cm
- Right vertical: 16 cm
- Inner horizontal (leftward): 16 cm
- Inner vertical (upward): 3 cm
- Top horizontal: 18 cm
- Left vertical: 19 cm

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

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

Is that right? Let me double-check.

Another way: the perimeter can be calculated as twice the sum of max width and max height, but adjusted for the cut.

Max width = 18 + 16 = 34 cm, max height = 19 cm, but since it's L-shaped, perimeter = 2*(34 + 19) - 2*overlap, but overlap is the inner corner.

Standard formula for L-shape: if you have outer dimensions, but here it's easier to stick with tracing.

Note that the inner vertical is 3 cm, which we have.

So 34+16+16+3+18+19= let's add again: 34+19=53, 16+18=34, 16+3=19, then 53+34=87, +19=106 cm. Yes.

So for 3) 106 cm.

4) T-shape or something.

Labels:
- Top horizontal: 12 m
- Right-vertical of top: 12 m
- Bottom horizontal: 24 m
- Left-vertical of bottom: 2 m? Wait, "2 m" on left, but that might be the height of the bottom part.
- Also "10 m" and "6 m" on the right.

Let's interpret.

It looks like a cross or T-shape.

From the labels:

- The top bar: width 12 m, height 12 m? But "12 m" on top and "12 m" on right of top, so probably the top rectangle is 12m x 12m.

Then below it, a wider base.

On the left, "2 m" — likely the height of the left part of the base.

On the right, "10 m" and "6 m" — perhaps the base has total height 6 m, and the right extension is 10 m wide or something.

Let's trace the perimeter.

Start at bottom-left corner.

- Move right along bottom: 24 m (given)
- Move up along right side: 6 m (given, since "6 m" on right)
- Move left along the top of the right part: but there's a label "10 m", which might be the width of the right protrusion.
- Then move up along the inner vertical: but how much?
- Then move left along the top of the middle part.
- Then move down along the left side.

This is messy.

From the diagram description:

- The bottom is 24 m wide.
- The left side has a short vertical of 2 m, then it goes right, then up, etc.

Perhaps the shape is composed of a large rectangle at bottom 24m wide and 6m high, and on top of it, centered or something, a smaller rectangle 12m wide and 12m high, but then the left side has "2 m", which might mean that the bottom rectangle extends 2 m above on the left? That doesn't make sense.

Another interpretation: the "2 m" is the height of the left wing, "6 m" is the height of the right wing, and the top is 12m, with 12m down on the right of the top.

Let's list all labeled segments:

- Top: 12 m (horizontal)
- Right of top: 12 m (vertical down)
- Then from there, it goes left 10 m (horizontal)
- Then down 6 m (vertical) — but "6 m" is labeled on the far right, so perhaps that's the total height on right.
- Bottom: 24 m
- Left: 2 m (vertical up from bottom)

Also, "10 m" is labeled on the horizontal between the top and bottom on the right.

So, likely, the shape has:

- A bottom rectangle 24 m wide and 6 m high? But then the left has only 2 m, so perhaps the bottom is not full height.

Assume the following structure:

The shape has a central column or something.

From bottom-left:

- Up 2 m (left side)
- Right ?
- Up to the top level
- Etc.

Perhaps it's better to calculate the total perimeter by adding all outer edges.

Let me define the points.

Suppose we start at bottom-left corner A.

- From A, move right along bottom to B: 24 m
- From B, move up to C: 6 m (since "6 m" on right)
- From C, move left to D: this should be the width of the right part. Label "10 m" is there, so perhaps CD = 10 m
- From D, move up to E: this is the height from the bottom of the top part to the top. Since the top has height 12 m, and the bottom has height 6 m on right, but on left it's 2 m, so the rise from D to E might be 12 - (6 - 2) or something. This is complicated.

Notice that the top part is 12 m wide and 12 m high, and it sits on top of the bottom part.

The bottom part is 24 m wide, and its height varies: on left, from bottom to the start of the top part is 2 m, on right, from bottom to the start of the top part is 6 m? But that would mean the top part is not level, which is unlikely.

Perhaps the "2 m" and "6 m" are the heights of the side extensions.

Another common configuration: the shape is like a capital T, but rotated or something.

Let's look at the labels again: "12 m" on top, "12 m" on the right of the top, "10 m" on the horizontal below that, "6 m" on the far right vertical, "24 m" on bottom, "2 m" on the left vertical.

So, likely, the left side has a vertical segment of 2 m from bottom, then it turns right, then up to meet the top part.

Similarly on right, from bottom up 6 m, then left 10 m, then up to the top.

And the top is 12 m wide.

So, the total height on left: from bottom to top is 2 m + height of top part. The top part has height 12 m, so total left height = 2 + 12 = 14 m? But not labeled.

For perimeter, we don't need total height, just the outer path.

Start at bottom-left corner P.

- Move right along bottom to Q: 24 m
- Move up along right side to R: 6 m
- Move left along the top of the right base to S: 10 m (label "10 m")
- Move up along the inner vertical to T: this distance is the height from the top of the right base to the bottom of the top part. Since the top part is 12 m high, and on the right, the base is 6 m high, but the top part starts at a certain level.

Actually, the top part is sitting on top of the base, so the vertical distance from S to T should be the difference in height between the top of the base and the bottom of the top part, but if the top part is directly on top, it should be zero, but that can't be.

Perhaps the "12 m" on the right of the top is the height of the top rectangle, so from its bottom to top is 12 m.

The base on the right is 6 m high, so if the top rectangle is placed on top of the base, then the total height on right is 6 + 12 = 18 m, but on left, the base is only 2 m high, so the top rectangle must be elevated or something.

This is inconsistent.

Perhaps the "2 m" and "6 m" are the heights of the side arms, and the top is separate.

Let's calculate the missing lengths.

From the bottom, width 24 m.

On the left, there is a vertical rise of 2 m, then it goes right for some distance, then up to the top level.

On the right, vertical rise of 6 m, then left for 10 m, then up to the top level.

The top is 12 m wide.

So, the distance between the left and right inner corners at the base level.

Let me denote:

Let the bottom be from x=0 to x=24.

At x=0, y=0 (bottom-left).

Move up to (0,2) — since 2 m up.

Then move right to (a,2) for some a.

Then move up to (a,b) , but b should be the bottom of the top part.

Similarly, at x=24, y=0, move up to (24,6) — 6 m up.

Then move left to (c,6) , and c = 24 - 10 = 14 m, since "10 m" leftward.

Then move up to (14,d).

The top part is from x=p to x=q, width 12 m, and height 12 m, so from y=e to y=e+12.

Probably, the top part is centered or aligned.

Likely, the top part starts at y=6 on the right, but on left at y=2, so it's not level, which is odd.

Perhaps the "12 m" on the right of the top is not the height, but the length of the side.

Another idea: perhaps the shape is symmetric or has specific proportions.

Let's assume that the top rectangle is 12 m wide and 12 m high, and it is positioned such that its bottom is at y=h.

On the left, the base rises to y=2 at x=0, then goes right to x=w, then up to y=h.

On the right, base rises to y=6 at x=24, then goes left to x=24-10=14, then up to y=h.

The top rectangle is from x=s to x=s+12, and y=h to y=h+12.

For the shape to be connected, the left inner corner at (w,2) must connect to the top rectangle, so probably w = s, and h >2.

Similarly, on right, (14,6) connects to top rectangle, so s+12 = 14, thus s = 2.

Then the top rectangle is from x=2 to x=14, width 12 m, good.

Then on left, from (0,2) move right to (2,2), then up to (2,h).

On right, from (24,6) move left to (14,6), then up to (14,h).

The top rectangle is from y=h to y=h+12.

Now, the height h is not given, but for the perimeter, we need the vertical distances.

From (2,2) to (2,h): distance |h-2|

From (14,6) to (14,h): distance |h-6|

Since the top is above, h >6 >2, so h-2 and h-6.

But h is not known. However, in the diagram, the "12 m" on the right of the top might be the height of the top rectangle, which is 12 m, so from y=h to y=h+12, so the side is 12 m, which is given, so that's consistent, but h is still unknown.

For the perimeter, when we go from (2,2) up to (2,h), then along the top of the top rectangle to (14,h+12)? No.

Let's trace the outer boundary.

Start at (0,0) — bottom-left.

- Move right to (24,0): 24 m
- Move up to (24,6): 6 m
- Move left to (14,6): 10 m (since 24-14=10)
- Move up to (14,h): distance h-6
- Move left to (2,h): distance 12 m (since 14-2=12, and this is the bottom of the top rectangle? No, at y=h, from x=14 to x=2 is 12 m, but this is the bottom side of the top rectangle, which is internal if the top rectangle is solid, but for perimeter, if it's the outer boundary, when we move from (14,h) to (2,h), that is along the bottom of the top rectangle, but if the top rectangle is above, this might be internal.

I think I have a mistake.

In a compound shape, the perimeter is the outer boundary, so for the top rectangle, its bottom side is not part of the perimeter if it's attached to the base.

In this case, the top rectangle is sitting on top of the base, so the bottom side of the top rectangle is internal and not part of the perimeter.

So, the outer boundary should go around the outside.

From (14,6) , after moving left to (14,6), then up to (14,h), but then instead of going left, we should go up along the right side of the top rectangle.

Let's redefine.

After reaching (14,6), we move up to (14,h) — this is the left side of the right base extension, but then at (14,h), we are at the bottom-right corner of the top rectangle.

Then, since the top rectangle is there, we move up along its right side to (14,h+12) — and "12 m" is labeled on the right of the top, so yes, this side is 12 m.

Then move left along the top to (2,h+12) — distance 12 m (width of top).

Then move down along the left side of the top rectangle to (2,h) — distance 12 m.

Then from (2,h), we need to go down to the base. On the left, from (2,h) down to (2,2) — distance h-2, then left to (0,2) — distance 2 m (since from x=2 to x=0), then down to (0,0) — distance 2 m.

But we have "2 m" labeled on the left, which is likely the vertical from (0,0) to (0,2).

So, let's list all segments for perimeter:

1. Bottom: (0,0) to (24,0): 24 m
2. Right-bottom vertical: (24,0) to (24,6): 6 m
3. Right-inner horizontal: (24,6) to (14,6): 10 m
4. Right-inner vertical: (14,6) to (14,h): let's call this V_r = h-6
5. Right-top vertical: (14,h) to (14,h+12): 12 m (given)
6. Top horizontal: (14,h+12) to (2,h+12): 12 m (width)
7. Left-top vertical: (2,h+12) to (2,h): 12 m (height of top)
8. Left-inner vertical: (2,h) to (2,2): V_l = h-2
9. Left-inner horizontal: (2,2) to (0,2): 2 m (since from x=2 to x=0)
10. Left-bottom vertical: (0,2) to (0,0): 2 m (given)

Now, we have V_r = h-6, V_l = h-2, but h is unknown.

However, in the diagram, there is no other label, so perhaps h is such that the shape is closed, but we have all sides except these two, but they depend on h.

Unless the "12 m" on the right of the top includes something, but it's labeled as the side.

Perhaps the top rectangle's height is 12 m, but the position is fixed by the connections.

Notice that from (2,2) to (2,h) and from (14,6) to (14,h), and the top is from y=h to y=h+12, but for the shape to be valid, the only constraint is that h >6, but no value given.

This suggests that in the actual diagram, the vertical distances are given or can be inferred.

Perhaps the "12 m" on the right of the top is not the height, but the length from the bottom of the top to the top, but in the context, it's likely the height.

Another possibility: the "12 m" labeled on the right of the top is the entire right side from bottom to top, but that would include the base and the top, but on right, from y=0 to y=6 is 6 m, then from y=6 to y=h is V_r, then from y=h to y=h+12 is 12 m, so total right side would be 6 + V_r + 12, but it's not labeled as such.

I think there's a mistake in my assumption.

Let's look back at the user's description for shape 4: "12 m" on top, "12 m" on the right of the top, "10 m" on the horizontal, "6 m" on the far right, "24 m" on bottom, "2 m" on the left.

Perhaps the "12 m" on the right of the top is the height of the top rectangle, and the "6 m" is the height of the right base, and "2 m" is the height of the left base, and the top rectangle is positioned so that its bottom is at the same level as the top of the bases, but since bases have different heights, it's not possible unless the top rectangle is not horizontal, which is unlikely.

Perhaps the "2 m" and "6 m" are not heights, but widths or something else.

Another idea: perhaps the shape is like a staircase or has steps.

Let's calculate the perimeter by adding all labeled sides and inferring the unlabeled ones.

Labeled sides:
- Top: 12 m
- Right of top: 12 m
- Inner horizontal: 10 m
- Far right vertical: 6 m
- Bottom: 24 m
- Left vertical: 2 m

Also, there must be other sides.

From the geometry, the left side has a vertical of 2 m, then a horizontal to the right, then a vertical up to the top level.

Similarly on right, vertical 6 m, horizontal left 10 m, vertical up to top level.

The top is 12 m wide.

The distance between the left and right inner vertical lines.

On the bottom, width 24 m.

On the left, after rising 2 m, it goes right for a distance, say A m.

On the right, after rising 6 m, it goes left for 10 m.

Then the top is 12 m wide, so the distance between the left inner vertical and right inner vertical at the top level is 12 m.

At the base level, the distance between the left inner point and right inner point is the bottom width minus the left overhang and right overhang, but it's complicated.

Let the left inner vertical be at x=L, right inner vertical at x=R.

From bottom, at x=0, y=0, up to (0,2), then right to (L,2), then up to (L,H) where H is the bottom of the top rectangle.

Similarly, at x=24, y=0, up to (24,6), then left to (R,6), then up to (R,H).

The top rectangle is from x=L to x=R, width R-L = 12 m (since top is 12 m wide).

Also, from the right, R = 24 - 10 = 14 m, because from x=24, move left 10 m to x=14.

So R = 14 m.

Then L = R - 12 = 14 - 12 = 2 m.

So left inner vertical at x=2 m.

Then from (0,2) to (2,2): distance 2 m (horizontal).

From (2,2) to (2,H): distance H-2

From (2,H) to (2,H+12): 12 m (left side of top)

From (2,H+12) to (14,H+12): 12 m (top)

From (14,H+12) to (14,H): 12 m (right side of top) — but this is already included in the "12 m" on the right of the top? The "12 m" is likely this side.

From (14,H) to (14,6): distance H-6

From (14,6) to (24,6): 10 m (already have)

From (24,6) to (24,0): 6 m

From (24,0) to (0,0): 24 m

From (0,0) to (0,2): 2 m

Now, the only unknowns are H-2 and H-6.

But in the perimeter, we have to include them, but H is not given.

However, in the diagram, there is no other label, so perhaps for the perimeter, these vertical segments are part of it, but we need their lengths.

Unless the top rectangle's height is 12 m, but H is the y-coordinate of its bottom, which is not specified.

Perhaps the "12 m" on the right of the top is the entire right side from y=0 to y=top, but that would be 6 + (H-6) + 12 = H +12, and if it's labeled 12 m, then H+12 = 12, so H=0, impossible.

I think there's a standard way or I need to assume that the vertical segments from the base to the top rectangle are given by the difference, but in this case, for the perimeter to be calculable, perhaps the shape is such that the top rectangle is at a height where the vertical drops are zero, but that can't be.

Another possibility: the "2 m" and "6 m" are the lengths of the horizontal segments, not vertical.

Let's read the user's input: "4) 12 m 12 m 2 m 10 m 6 m 24 m" and "Perimeter:"

In the text, it's "12 m" on top, "12 m" on the right of the top, "2 m" on the left, "10 m" on the horizontal, "6 m" on the right, "24 m" on bottom.

Perhaps "2 m" is the height of the left part, "6 m" is the height of the right part, and the top is 12 m high, and the horizontal "10 m" is the width of the right arm.

Then, the total height on left is 2 + 12 = 14 m, on right 6 + 12 = 18 m, but then the top is not level.

For perimeter, when we go up the left, we go 2 m up, then right, then 12 m up, etc.

Let's try that.

Start at bottom-left (0,0).

- Move right to (24,0): 24 m
- Move up to (24,6): 6 m (right base height)
- Move left to (24-10,6) = (14,6): 10 m
- Move up to (14,6+12) = (14,18): 12 m (top right side)
- Move left to (2,18): 12 m (top width, since 14-2=12)
- Move down to (2,2): 16 m? From y=18 to y=2 is 16 m, but on left, the base is only 2 m high, so from (2,18) down to (2,2) is 16 m, then left to (0,2): 2 m, then down to (0,0): 2 m.

But the "2 m" on left is likely the vertical from (0,0) to (0,2), so that's given.

So sides:
1. 24 m (bottom)
2. 6 m (right-bottom vertical)
3. 10 m (right-inner horizontal)
4. 12 m (right-top vertical)
5. 12 m (top horizontal)
6. 16 m (left-top vertical) — from y=18 to y=2
7. 2 m (left-inner horizontal) — from x=2 to x=0
8. 2 m (left-bottom vertical) — from y=2 to y=0

Sum: 24+6=30; +10=40; +12=52; +12=64; +16=80; +2=82; +2=84 m.

But is the left-top vertical 16 m? From y=2 to y=18 is 16 m, yes.

And the top is from y=6 to y=18 on right, but on left from y=2 to y=18, so the top rectangle is not rectangular; it's skewed, but in the diagram, it's probably intended to be rectangle, so this may not be correct.

Perhaps the top rectangle is at a constant height, so H is the same, and the vertical segments are H-2 and H-6, but H is not given, so perhaps in the diagram, the "12 m" on the right of the top is the only height given, and the base heights are given, but for the perimeter, we can express, but we need a number.

I recall that in some worksheets, for shape 4, the perimeter is 84 m or 88 m, but let's calculate with the values.

Another way: perhaps the "12 m" on the right of the top is the height, and the base heights are 2 m and 6 m, and the top is aligned at the top, so the bottom of the top rectangle is at y= max(2,6) =6 m on right, but on left, from y=2 to y=6, there is a vertical segment.

So, on left, from (0,0) to (0,2): 2 m
then to (2,2): 2 m (horizontal)
then to (2,6): 4 m (vertical, since 6-2=4)
then to (2,18): 12 m (up to top of top rectangle, if top is 12 m high from y=6 to y=18)
then to (14,18): 12 m
then to (14,6): 12 m (down)
then to (24,6): 10 m
then to (24,0): 6 m
then to (0,0): 24 m

But from (14,6) to (24,6) is 10 m, already have, and from (24,0) to (0,0) is 24 m, but we have from (0,0) to (0,2) etc.

Let's list unique segments:

- (0,0) to (0,2): 2 m
- (0,2) to (2,2): 2 m (assume, since L=2)
- (2,2) to (2,6): 4 m (6-2=4)
- (2,6) to (2,18): 12 m (height of top)
- (2,18) to (14,18): 12 m (top)
- (14,18) to (14,6): 12 m (right side of top)
- (14,6) to (24,6): 10 m
- (24,6) to (24,0): 6 m
- (24,0) to (0,0): 24 m

Sum: 2+2+4+12+12+12+10+6+24 = let's calculate: 2+2=4; +4=8; +12=20; +12=32; +12=44; +10=54; +6=60; +24=84 m.

Same as before.

And the "2 m" on left is used, "6 m" on right, "10 m" inner, "12 m" top, "12 m" right of top, "24 m" bottom, and the additional 2 m horizontal on left, and 4 m vertical on left, but the 4 m is not labeled, but in the calculation, it's derived.

In the diagram, the 4 m might not be labeled, but for perimeter, we include it.

So perimeter = 84 m for shape 4.

I think that's reasonable.

So for 4) 84 m.

5) Trapezoid or irregular quadrilateral.

Labels:
- Left vertical: 4 m
- Bottom horizontal: 4 m
- Right vertical: 2 m
- Top slant: 16 m

So sides: 4 m, 4 m, 2 m, 16 m.

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

Is that it? Seems straightforward.

But is the top slant the only top side? Yes, it's a quadrilateral with those four sides.

So 4+4+2+16=26 m.

6) Trapezoid.

Labels:
- Left vertical: 11 m
- Bottom horizontal: 20 m
- Right slant: 14 m
- Top horizontal: 9 m

So sides: 11, 20, 14, 9.

Perimeter = 11+20+14+9 = 54 m.

7) Pentagon or house shape.

Labels:
- Left slant: 12 cm
- Right slant: 16 cm
- Right vertical: 5 cm
- Bottom horizontal: 14 cm
- Left vertical: ? not labeled, but probably the same as right or something.

From the shape, it's like a rectangle with a triangle on top.

So, bottom: 14 cm
Right side: 5 cm (vertical)
Left side: should be the same as right if symmetric, but not specified.

Top has two slants: 12 cm and 16 cm.

So likely, the left vertical is not given, but in such shapes, the left and right verticals are equal, but here right is 5 cm, left might be different.

Perhaps the left vertical is part of the slant.

Let's assume the shape has:

- Bottom: 14 cm
- Right vertical: 5 cm
- Then right slant: 16 cm to the apex
- Then left slant: 12 cm down to the left top
- Then left vertical down to bottom-left.

But the left vertical is not labeled.

Perhaps the left vertical is the same as right, 5 cm, but then the slants would be from the top of the verticals to the apex.

So, if left vertical is 5 cm, right vertical is 5 cm, bottom 14 cm, then the top has two slants: 12 cm and 16 cm.

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

But is the left vertical 5 cm? Not specified, but in many such problems, it is assumed symmetric or given.

Perhaps from the diagram, the left vertical is not there; instead, the left slant starts from the bottom-left.

Let's think: if it's a pentagon with vertices at bottom-left, bottom-right, top-right, apex, top-left.

Then sides:
- Bottom: 14 cm
- Right vertical: 5 cm (from bottom-right to top-right)
- Right slant: 16 cm (from top-right to apex)
- Left slant: 12 cm (from apex to top-left)
- Left vertical: from top-left to bottom-left — not labeled.

So we need that length.

Perhaps in the diagram, the left vertical is equal to the right vertical, 5 cm, or perhaps it's different.

Another possibility: the "5 cm" is the height of the rectangle part, and the slants are the roof.

But still, the left vertical should be given or inferred.

Perhaps the left vertical is not present; the left slant goes directly from apex to bottom-left, but then the right side has a vertical, which is inconsistent.

I think for standard problems, the left and right verticals are both 5 cm, so perimeter = 5 + 12 + 16 + 5 + 14 = 52 cm.

Or perhaps the 5 cm is only on right, and on left, it's different.

Let's calculate the missing side.

Suppose the bottom is 14 cm.

Let the left vertical be H_l, right vertical H_r = 5 cm.

Then the horizontal distance between the top of left vertical and top of right vertical is 14 cm, since bottom is 14 cm and verticals are perpendicular.

Then the apex is above, with slant to left top 12 cm, to right top 16 cm.

Then the distance between left top and right top is 14 cm.

So we have a triangle with sides 12, 16, and base 14 cm.

But for perimeter, we need the outer sides, which include the verticals and the slants and bottom.

So perimeter = H_l + 12 + 16 + H_r + 14 = H_l + 5 + 12 + 16 + 14 = H_l + 47.

But H_l is unknown.

Unless H_l = H_r = 5 cm, then 52 cm.

Perhaps in the diagram, the left vertical is labeled or implied to be 5 cm.

I think for the sake of time, I'll assume it's 5 cm, so 52 cm.

8) T-shape or something.

Labels:
- Top horizontal: 36 m
- Right-vertical of top: 36 m
- Bottom horizontal: 60 m
- Right-vertical of bottom: 36 m
- Also, the left part.

From the description, it's like a plus sign or T.

"36 m" on top, "36 m" on right of top, "36 m" on right of bottom, "60 m" on bottom.

Probably, the shape has a top rectangle 36m x 36m, and a bottom rectangle 60m wide and 36m high, but then the right side has "36 m" for both, so perhaps the bottom rectangle is 60m wide, 36m high, and the top rectangle is centered on top, 36m wide, 36m high.

Then the left side will have overhang.

So, total width 60 m, top width 36 m, so overhang on left and right: (60-36)/2 = 12 m on each side.

Height: bottom 36 m, top 36 m, so total height 72 m.

For perimeter, trace the boundary.

Start at bottom-left.

- Move right along bottom: 60 m
- Move up along right side: 36 m (height of bottom rectangle)
- Move left along the top of the bottom rectangle: but since the top rectangle is on top, at y=36, from x=0 to x=60, but the top rectangle is from x=12 to x=48 (since 60-36=24, /2=12 on each side), so from x=60 to x=48: 12 m (leftward)
- Move up along the right side of the top rectangle: 36 m (to y=72)
- Move left along the top: 36 m (to x=12