Math worksheet for calculating area and perimeter of rectilinear shapes by dividing into rectangles.

Let’s solve each problem step by step. We’ll find missing sides, split shapes into rectangles, calculate area and perimeter carefully.

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Problem 1)

Shape is L-shaped. Given:
- Top horizontal = 5 cm
- Right vertical = 7 cm
- Left vertical part = 6 cm (from top down to the “step”)
- Bottom left horizontal = 8 cm

We need to find missing sides.

First, total height on right is 7 cm. The left side has a 6 cm segment going down from top — so the bottom part of the left side must be 7 - 6 = 1 cm.

Total width at bottom: we have 8 cm on the left, and the top part is 5 cm wide — so the right part of the bottom must be 5 cm? Wait — let’s think differently.

Actually, look at the shape:

It’s like a big rectangle with a smaller rectangle cut out from the bottom left? Or better — split it into two rectangles.

Option 1: Split vertically.

Left rectangle: width = 8 cm, height = ? → but we don’t know full height yet.

Better: Split horizontally.

Top rectangle: width = 5 cm, height = 6 cm → Area = 5 × 6 = 30 cm²

Bottom rectangle: extends under the top one. Its width = 8 + 5 = 13 cm? No — wait.

Actually, the bottom part goes all the way across. From left to right: 8 cm (left arm) plus the part under the top rectangle. Since top rectangle is 5 cm wide, and sits on the right, then the bottom rectangle’s width is 8 + 5 = 13 cm? But that doesn’t match the right side being 7 cm tall.

Wait — let’s label all sides.

Start from top-left corner.

Go right 5 cm → then down 6 cm → then right ??? → then down ??? → then left ??? → then up ???.

Actually, easier: use the fact that opposite sides in rectilinear shapes add up.

Total height on right = 7 cm. On left, we have a 6 cm drop, then a small vertical drop to complete the 7 cm → so that small drop is 1 cm.

Total width at bottom: we have 8 cm on the left, and the top part is 5 cm — so the bottom must extend 5 cm under the top part? So total bottom width = 8 + 5 = 13 cm? But then the right side is only 7 cm tall — which matches.

But wait — if bottom width is 13 cm, and top width is 5 cm, then the “step” on the right must account for the difference.

Actually, let’s draw mentally:

Imagine the full bounding box: width = 8 + 5 = 13 cm? Height = 7 cm.

But there’s a notch on the bottom left? No — actually, the shape is like:

From top-left: go right 5 cm, down 6 cm, then right X cm, then down Y cm, then left Z cm, then up W cm to close.

Given: after going down 6 cm, we go right — how far? The total bottom length is not given, but we know the leftmost bottom is 8 cm long.

Actually, standard way: the horizontal segments must balance.

Top horizontal: 5 cm

Bottom horizontal: should equal top + any extensions. Here, the bottom has a segment of 8 cm on the left, and then continues under the top part. Since the top part is 5 cm wide, and aligned to the right, then the bottom must be 8 + 5 = 13 cm total? But that would mean the right side is straight down 7 cm — which it is.

But then what about the verticals?

Left side: from bottom to the step: since total height is 7 cm, and from top to step is 6 cm, then from step to bottom is 1 cm.

So now we can split the shape into two rectangles:

Rectangle A (top): 5 cm wide × 6 cm high → Area = 30 cm²

Rectangle B (bottom): spans entire width? Width = 8 cm (left part) + 5 cm (under top) = 13 cm? But height is only 1 cm → Area = 13 × 1 = 13 cm²

Total area = 30 + 13 = 43 cm²

But wait — is the bottom rectangle really 13 cm wide? Let’s check the right side.

The right side is 7 cm tall. The top rectangle takes 6 cm of that, so the bottom rectangle adds 1 cm below it — yes.

And horizontally: the bottom rectangle starts at left edge and goes all the way to right edge — which is 8 cm (left arm) plus the 5 cm under the top rectangle — so yes, 13 cm.

But is that correct? Let’s verify with another split.

Split vertically:

Left rectangle: width 8 cm, height 1 cm (the bottom part) → Area = 8 × 1 = 8 cm²

Right rectangle: width 5 cm, height 7 cm → Area = 5 × 7 = 35 cm²

Total area = 8 + 35 = 43 cm² — same! Good.

Now perimeter.

Perimeter is the total distance around the outside.

List all outer sides:

Start at top-left corner:

- Right 5 cm

- Down 6 cm

- Right ? How much? From the vertical split, the right rectangle is 5 cm wide, left is 8 cm, so when we go down 6 cm from top-right of left part, we need to go right to connect to the right rectangle. Actually, in the shape, after going down 6 cm, we go right — how far? It should be the difference between the total width and the left part? Total width is 13 cm, left part is 8 cm, so we go right 5 cm? But that would be overlapping.

I think I made a mistake.

Let me define coordinates.

Set bottom-left corner as (0,0).

Then:

- Go right 8 cm to (8,0)

- Go up 1 cm to (8,1) [since total height is 7, and top part starts at y=1?]

Wait, better:

Assume the shape has:

- Bottom side: from (0,0) to (13,0)? But we don't know.

From the diagram description:

Typically in such problems, the 8 cm is the bottom-left horizontal, 6 cm is the left-vertical from top down to the step, 5 cm is the top-horizontal, 7 cm is the right-vertical.

So, let's assume:

- Start at top-left point A.

- Move right 5 cm to B.

- Move down 6 cm to C.

- Move right X cm to D.

- Move down Y cm to E.

- Move left Z cm to F.

- Move up W cm to A.

We know:

- AB = 5 cm (right)

- BC = 6 cm (down)

- DE = ? down

- EF = ? left

- FA = ? up

Also, the left side has a segment of 8 cm — that must be EF or part of it.

Actually, the 8 cm is labeled on the bottom-left horizontal, so that's probably EF.

Similarly, the right side is 7 cm, which is from B down to E? But B to C is 6 cm, so C to E must be 1 cm.

So:

- BC = 6 cm down

- CD = ? right — this should be the width of the "notch" or something.

Actually, from C, we go right to D, then down to E, then left to F, then up to A.

The distance from F to A is the left side, which should be 7 cm total, but we have BC = 6 cm, so if FA is vertical, it should be 7 cm, but that can't be because C is already 6 cm down.

I think the 7 cm is the full right side, from B to E.

So B to E is 7 cm down.

But B to C is 6 cm down, so C to E is 1 cm down.

Now, horizontally: from A to B is 5 cm right.

From F to A is up, and F is at the bottom-left.

The bottom-left horizontal is 8 cm, which is from F to some point, say G, but in the shape, from F we go right to E? Let's see.

Standard interpretation:

The shape has:

- Top: 5 cm

- Right: 7 cm

- Bottom: consists of two parts: left part 8 cm, and right part under the top, which should be 5 cm, so total bottom 13 cm? But then the left side: from bottom to the step is 1 cm (since 7-6=1), and from step to top is 6 cm.

So the vertical on the left is not continuous; it's broken.

For perimeter, we walk around:

Start at top-left corner.

- Right 5 cm (top)

- Down 6 cm (right side of top part)

- Right ? How much? This is the key. After going down 6 cm, we are at the "inner" corner. To go to the bottom-right, we need to go right and then down.

The total width at the bottom is the sum of the left arm and the part under the top. Since the top is 5 cm wide and sits on the right, the bottom must extend 5 cm under it, and the left arm is 8 cm, so the horizontal segment after going down 6 cm is the width of the "gap" — which is the difference between the total width and the left arm? Total width is not given.

Notice that the right side is 7 cm, and the left side has a 6 cm segment from top, so the remaining vertical on the left is 1 cm.

Horizontally, the top is 5 cm, and the bottom-left is 8 cm, so the bottom-right part must be such that the total width is consistent.

When we go from the end of the 6 cm down, we go right to align with the right side. Since the right side is straight down 7 cm, and we are at x=5 (if A is at x=0), then to reach the right side at x=5+ something.

Actually, the right side is at a fixed x-position. Let's set coordinates.

Set point A (top-left) at (0,7) — since total height is 7 cm.

Then:

- B: (5,7) // right 5 cm

- C: (5,1) // down 6 cm (since 7-6=1)

- Now, from C, we go right to D. How far? The bottom-left horizontal is 8 cm, which is from the left edge to the start of the rise. The left edge is at x=0, and the rise is at x=8? But we are at x=5.

This is confusing.

Perhaps the 8 cm is the length of the bottom-left horizontal segment, which is from (0,0) to (8,0), then up to (8,1), then right to (5,1)? That doesn't make sense.

Let's look for a different approach.

In rectilinear shapes, the perimeter can be found by adding all outer sides, and for area, split into rectangles.

From the vertical split I did earlier: left rectangle 8cm x 1cm, right rectangle 5cm x 7cm, area 8*1 + 5*7 = 8 + 35 = 43 cm² — that seems correct.

For perimeter, let's list the sides:

- Top: 5 cm

- Right: 7 cm

- Bottom: the bottom has two parts: from left to the step: 8 cm, and from the step to right: but the step is at x=8, and the right side is at x=5+ something.

If the right rectangle is 5 cm wide, and it's on the right, then its left edge is at x= total width - 5.

The left rectangle is 8 cm wide, so if they are adjacent, total width is 8 + 5 = 13 cm.

So:

- Bottom: from (0,0) to (13,0) — but is that true? In the shape, from (0,0) to (8,0) is the bottom-left, then from (8,0) to (8,1) up, then from (8,1) to (13,1) right? But then from (13,1) to (13,7) up, but the right side is only 7 cm, and we have from (5,7) to (5,1) down, which is not matching.

I think I have a fundamental mistake.

Let me search for a standard way.

Perhaps the 8 cm is the length of the bottom horizontal on the left, and the 5 cm is the top horizontal, and the 6 cm is the vertical on the left from top to the step, and 7 cm is the full right vertical.

So, the shape is like a capital L but rotated.

So, the total height is 7 cm.

The left side has a vertical segment of 6 cm from the top, so the bottom part of the left side is 7 - 6 = 1 cm.

The top has a horizontal of 5 cm.

The bottom has a horizontal of 8 cm on the left.

Now, the horizontal segment at the "step" level: from the end of the 6 cm down, we go right to meet the right side. The distance we go right is the difference between the total width and the 5 cm? But what is total width?

Notice that the bottom-left horizontal is 8 cm, and it is at the bottom, while the top is 5 cm at the top.

The right side is 7 cm, so the shape extends from y=0 to y=7.

At y=7, x from 0 to 5 (top).

At y=0, x from 0 to ? The bottom-left is 8 cm, so from x=0 to x=8 at y=0.

Then, at the step, which is at y=1 (since from y=7 down 6 cm to y=1), we have a horizontal segment from x=5 to x=8? Because from (5,1) to (8,1), then down to (8,0), then left to (0,0), but that would make the bottom from (0,0) to (8,0), and the left side from (0,0) to (0,7), but we have only 6 cm on the left from top, so from (0,7) to (0,1) is 6 cm, then from (0,1) to (0,0) is 1 cm, but in this case, from (0,1) to (8,1) is horizontal, then down to (8,0), then left to (0,0).

But then the right side is from (5,7) to (5,1) , which is 6 cm, but the problem says the right side is 7 cm, which would be from (5,7) to (5,0), but in this case, from (5,1) to (5,0) is not there; instead, we have from (5,1) to (8,1) to (8,0).

So the right side is not straight; it's only from (5,7) to (5,1), and then the rest is not on the right.

The problem says "7cm" on the right side, which likely means the full right edge is 7 cm, so it must be from top to bottom on the right.

So perhaps the 5 cm top is not at the left; let's assume the shape is oriented with the long part on the bottom.

Another common configuration: the 8 cm is the bottom, 7 cm is the right side, 5 cm is the top, 6 cm is the left side from top to the inner corner.

So, let's say:

- Bottom: 8 cm (horizontal)

- Right: 7 cm (vertical)

- Top: 5 cm (horizontal)

- Left: 6 cm (vertical from top to the step)

Then, the missing horizontal at the step level: since the bottom is 8 cm, and the top is 5 cm, and they are offset, the horizontal segment at the step must be 8 - 5 = 3 cm? Let's see.

From bottom-left: go right 8 cm to bottom-right.

Go up 7 cm to top-right.

Go left 5 cm to top-left of the top part.

Go down 6 cm to the step.

Then go left ? to meet the left side.

The left side from bottom to the step: since total height is 7 cm, and from top to step is 6 cm, so from step to bottom is 1 cm.

So from the step, we go left to the left side, which is at x=0, and we are at x=5 (if top-right is at x=8, then top-left of top part is at x=8-5=3, then down 6 cm to (3,1), then left to (0,1), then down to (0,0).

So the horizontal segment at y=1 is from x=3 to x=0, so 3 cm left.

So sides:

- Bottom: 8 cm (0,0) to (8,0)

- Right: 7 cm (8,0) to (8,7)

- Top: 5 cm (8,7) to (3,7) // left 5 cm

- Then down 6 cm (3,7) to (3,1)

- Then left 3 cm (3,1) to (0,1)

- Then down 1 cm (0,1) to (0,0)

Yes, that makes sense.

So missing sides are: the left-down from (0,1) to (0,0) = 1 cm, and the horizontal from (3,1) to (0,1) = 3 cm.

Now, area: split into two rectangles.

Rectangle 1: bottom part: from y=0 to y=1, x=0 to x=8 → width 8 cm, height 1 cm → area 8 cm²

Rectangle 2: top part: from y=1 to y=7, x=3 to x=8 → width 5 cm, height 6 cm → area 30 cm²

Total area = 8 + 30 = 38 cm²

Earlier I had 43, but that was wrong.

With this, area is 38 cm².

Verify with another split: left rectangle: x=0 to 3, y=1 to 7? But that's not a rectangle in the shape.

Or, the whole thing minus the missing part, but it's easier with the split above.

So area = 38 cm².

Perimeter: sum of all outer sides.

From above:

- Bottom: 8 cm

- Right: 7 cm

- Top: 5 cm

- Down: 6 cm

- Left-horizontal: 3 cm (from (3,1) to (0,1))

- Down-left: 1 cm (from (0,1) to (0,0))

But when we walk around, from (0,0) to (8,0): 8 cm

(8,0) to (8,7): 7 cm

(8,7) to (3,7): 5 cm (left)

(3,7) to (3,1): 6 cm (down)

(3,1) to (0,1): 3 cm (left)

(0,1) to (0,0): 1 cm (down)

Sum: 8+7+5+6+3+1 = let's calculate: 8+7=15, +5=20, +6=26, +3=29, +1=30 cm.

Is that correct? But in a closed shape, perimeter should be the boundary.

Notice that the path is continuous, and we have all sides.

We can also think of the perimeter as the sum of all external edges.

Another way: the shape has a bounding box of width 8 cm, height 7 cm, but with a notch on the top-left.

The notch is 3 cm wide and 6 cm high, but since it's indented, the perimeter increases.

Bounding box perimeter: 2*(8+7) = 30 cm, and since the notch is inside, but in this case, the notch is on the corner, so when we indent, we remove two sides but add two new sides of the same length, so perimeter remains the same as bounding box.

Bounding box 8x7, perimeter 2*(8+7)=30 cm, and our calculation gave 30 cm, so yes.

In this case, the indentation is at the top-left, but since we are removing a rectangle from the corner, the perimeter doesn't change because the two new sides replace the two removed sides.

Here, we removed a 3cm by 6cm rectangle from the top-left corner of the 8x7 rectangle, but in our shape, it's not removed; it's that the shape is the L-shape, which is equivalent to the 8x7 rectangle minus a 3x6 rectangle at the top-left? Let's see.

If we have a full 8x7 rectangle, area 56 cm².

Remove a rectangle at top-left: from x=0 to 3, y=1 to 7, which is 3x6=18 cm², so area 56-18=38 cm², matches.

Perimeter of full rectangle is 30 cm. When we remove a corner rectangle, we remove two sides: the top 3 cm and the left 6 cm, but we add the new internal sides: the bottom of the removed rectangle (3 cm) and the right of the removed rectangle (6 cm), so net change 0, so perimeter still 30 cm.

Perfect.

So for problem 1:

Area = 38 cm²

Perimeter = 30 cm

But the question asks for perimeter in meters? No, look: "Perimeter = ____ m" — but the units are cm, so probably a typo, or perhaps they want it in meters, but 30 cm is 0.3 m, but that seems odd.

Look back at the image description: for problem 1, it says "Perimeter = ____ m", but all dimensions are in cm, so likely a mistake, or perhaps they want it in meters, but that would be unusual.

In the user's message, for problem 1: "Perimeter = ____ m" , but areas are in cm², so probably it's a typo, and should be cm.

Similarly, for problem 2, it asks for perimeter in mm, while dimensions are in m.

So we'll compute as per units given.

For problem 1, perimeter is 30 cm, but they ask for m, so 30 cm = 0.3 m.

But let's confirm the area first.

Area = 38 cm², as calculated.

Now, for perimeter, if they want in meters, 30 cm = 0.3 m.

But let's see other problems.

Perhaps for problem 1, it's a mistake, and should be cm.

To be safe, we'll calculate as per instruction.

But in the answer blank, it says "Perimeter = ____ m", so we'll put 0.3.

But let's double-check the shape.

In my coordinate system:

Points: (0,0), (8,0), (8,7), (3,7), (3,1), (0,1), back to (0,0).

Sides:

- (0,0)-(8,0): 8 cm

- (8,0)-(8,7): 7 cm

- (8,7)-(3,7): 5 cm (since 8-3=5)

- (3,7)-(3,1): 6 cm (7-1=6)

- (3,1)-(0,1): 3 cm (3-0=3)

- (0,1)-(0,0): 1 cm (1-0=1)

Sum: 8+7+5+6+3+1 = 30 cm, yes.

Area: as above, 38 cm².

So for problem 1:

Area = 38 square cm

Perimeter = 30 cm = 0.3 m (since 1 m = 100 cm)

But typically in such worksheets, they might expect cm, but the blank says "m", so we'll go with 0.3.

Perhaps it's a typo, but we'll follow the text.

Now, problem 2.

Problem 2)

Dimensions: 0.9m, 1m, 0.5m, 0.4m

Shape is like a rectangle with a bite taken out of the bottom-right or something.

Given:

- Left side: 0.9m

- Bottom: 1m

- Right side: 0.5m (but this is only part of it)

- And 0.4m on the top-right or something.

From the description: "0.9m" on left, "1m" on bottom, "0.5m" on right, "0.4m" on the top of the notch.

Likely, the shape is a rectangle with a rectangular notch on the bottom-right.

So, full height on left is 0.9m.

Full width on bottom is 1m.

On the right, the vertical side is 0.5m, which is probably the top part, and then there's a horizontal 0.4m going left, then down to the bottom.

So, similar to before.

Let me define.

Assume bottom-left (0,0).

Go right 1m to (1,0).

Go up ? to (1,h), but right side is given as 0.5m, but that might not be full height.

The 0.5m is labeled on the right, and 0.4m on the top of the notch.

Probably, from top-right, go down 0.5m, then left 0.4m, then down to bottom.

And left side is 0.9m.

So, total height is 0.9m.

From top-right, down 0.5m to a point, then left 0.4m, then down to bottom.

The down from there to bottom should be 0.9 - 0.5 = 0.4m.

Then, the bottom is 1m, but after going left 0.4m from the right, we are at x=1-0.4=0.6m, then down to (0.6,0), then left to (0,0), but the bottom is from (0,0) to (1,0), so from (0.6,0) to (1,0) is part of it, but we have a segment from (0.6,0) to (0.6,0.4) up? Let's see.

Points:

Start at top-left (0,0.9)

Go right to (w,0.9) — what is w? Not given directly.

From the right side: from top-right (a,0.9) down to (a,0.4) since 0.9-0.5=0.4? If down 0.5m, to y=0.4.

Then left 0.4m to (a-0.4,0.4)

Then down to (a-0.4,0)

Then left to (0,0)

Then up to (0,0.9)

The bottom is from (0,0) to (a-0.4,0), and this is given as 1m? The bottom is labeled 1m, so distance from (0,0) to (a-0.4,0) is 1m, so a-0.4 = 1, thus a = 1.4m.

Then, the top is from (0,0.9) to (1.4,0.9), so width 1.4m.

Left side 0.9m, good.

Right side: from (1.4,0.9) to (1.4,0.4) = 0.5m, good.

Then from (1.4,0.4) to (1.0,0.4) = 0.4m left.

Then from (1.0,0.4) to (1.0,0) = 0.4m down.

Then from (1.0,0) to (0,0) = 1.0m left? But the bottom is labeled 1m, which is from (0,0) to (1.0,0), yes.

In the shape, the bottom is from (0,0) to (1.0,0), but according to this, from (0,0) to (1.0,0) is 1m, and from (1.0,0) to (1.4,0) is not there; instead, from (1.0,0) we go up to (1.0,0.4), etc.

The bottom side is only from (0,0) to (1.0,0), length 1m, as given.

Then from (1.0,0) up to (1.0,0.4), then right to (1.4,0.4), then up to (1.4,0.9), then left to (0,0.9), then down to (0,0).

But the left side is from (0,0.9) to (0,0) = 0.9m, good.

Now, the side from (1.0,0.4) to (1.4,0.4) is 0.4m, as given.

And from (1.4,0.9) to (1.4,0.4) is 0.5m, good.

So missing sides: the vertical from (1.0,0) to (1.0,0.4) = 0.4m, and the horizontal from (0,0.9) to (1.4,0.9) = 1.4m, but that's not missing; it's implied.

For area, split into rectangles.

One way: the main rectangle minus the notch, or add parts.

Rectangle 1: left part: from x=0 to 1.0, y=0 to 0.9 → width 1.0m, height 0.9m → area 0.9 m²

But there is a part on the right: from x=1.0 to 1.4, y=0.4 to 0.9 → width 0.4m, height 0.5m → area 0.2 m²

Total area = 0.9 + 0.2 = 1.1 m²

Is that correct? The left rectangle includes from y=0 to 0.9, x=0 to 1.0, but in the shape, at x=1.0, from y=0 to 0.4 is present, and from y=0.4 to 0.9 is not in this rectangle; in this rectangle, it's filled, but in the actual shape, for x>1.0, only y>0.4 is present.

In my split, the left rectangle is x=0 to 1.0, y=0 to 0.9, which is fine, and the right rectangle is x=1.0 to 1.4, y=0.4 to 0.9, which is the top-right part.

And they don't overlap, and cover the shape.

Area = 1.0 * 0.9 + 0.4 * 0.5 = 0.9 + 0.2 = 1.1 m²

Another way: full rectangle if no notch: width 1.4m, height 0.9m, area 1.26 m²

Minus the notch: which is from x=1.0 to 1.4, y=0 to 0.4, size 0.4m x 0.4m = 0.16 m²

So area = 1.26 - 0.16 = 1.1 m², same.

Good.

Now perimeter.

Walk around:

Start at (0,0)

- Right to (1.0,0): 1.0 m

- Up to (1.0,0.4): 0.4 m

- Right to (1.4,0.4): 0.4 m

- Up to (1.4,0.9): 0.5 m

- Left to (0,0.9): 1.4 m

- Down to (0,0): 0.9 m

Sum: 1.0 + 0.4 + 0.4 + 0.5 + 1.4 + 0.9

Calculate: 1.0+0.4=1.4, +0.4=1.8, +0.5=2.3, +1.4=3.7, +0.9=4.6 m

As a check, bounding box 1.4m x 0.9m, perimeter 2*(1.4+0.9)=2*2.3=4.6 m, and since the notch is on the corner, perimeter unchanged, yes.

So perimeter = 4.6 m

But the question asks for perimeter in mm.

1 m = 1000 mm, so 4.6 m = 4600 mm.

Area = 1.1 m²

Now, problem 3.

Problem 3)

Dimensions: 2cm, 10cm, 55mm, 60mm

Units mixed: cm and mm.

Need to convert to same unit. Probably convert all to cm, since area asked in cm².

1 cm = 10 mm, so 55 mm = 5.5 cm, 60 mm = 6.0 cm.

Shape is L-shaped.

Given:

- Top-left horizontal: 2 cm

- Left vertical: 10 cm

- Then a horizontal segment: 60 mm = 6 cm

- And a vertical segment: 55 mm = 5.5 cm

Likely, from top-left, go right 2 cm, then down some, then right 6 cm, then down 5.5 cm, then left, then up.

Total height on left is 10 cm.

After going down from top, we have a horizontal of 6 cm, then down 5.5 cm.

So, the vertical from top to the first horizontal: let's say from (0,10) to (2,10) right 2 cm.

Then down to (2,y), then right to (2+6,y)=(8,y), then down to (8,y-5.5), then left to (0,y-5.5), then up to (0,10).

The left side from (0,y-5.5) to (0,10) is 10 cm, so the distance is 10 - (y-5.5) = 10 - y + 5.5 = 15.5 - y, but this should be the length, which is given as part of the 10 cm? The 10 cm is the full left side, so from (0,0) to (0,10), but in this case, the bottom is at y= y-5.5.

Assume bottom at y=0.

So, from (0,0) to (0,10) up.

But the shape may not start at (0,0).

From the description, likely the 10 cm is the left vertical, so from bottom to top on left is 10 cm.

Then, at the top, go right 2 cm.

Then down some distance, say d cm.

Then right 6 cm.

Then down 5.5 cm to the bottom.

Then left to the left side.

The total height is 10 cm, so the sum of the two down segments should be 10 cm.

From top, down d cm, then down 5.5 cm, so d + 5.5 = 10, thus d = 4.5 cm.

Then, horizontally, from left, at the top, we go right 2 cm, then after down d=4.5 cm, we go right 6 cm, so the total width at that level is 2 + 6 = 8 cm.

Then down 5.5 cm to bottom.

Then left to x=0.

So the bottom is from (0,0) to (8,0)? But when we go left from (8,0) to (0,0), but is that correct?

Points:

Start at top-left (0,10)

- Right to (2,10)

- Down to (2,10-4.5)=(2,5.5) [since d=4.5]

- Right to (2+6,5.5)=(8,5.5)

- Down to (8,5.5-5.5)=(8,0)

- Left to (0,0)

- Up to (0,10)

Yes.

So missing sides: the down from (2,10) to (2,5.5) = 4.5 cm, and the left from (8,0) to (0,0) = 8 cm, but that's not missing; it's implied.

For area, split into rectangles.

Rectangle 1: left part: x=0 to 2, y=0 to 10 → width 2 cm, height 10 cm → area 20 cm²

But this includes the part where there is no shape? No, in this region, from y=0 to 10, x=0 to 2, is it all filled? In the shape, from (0,0) to (0,10) to (2,10) to (2,5.5) to (8,5.5) to (8,0) to (0,0), so for x=0 to 2, y=0 to 10 is filled, yes.

Then rectangle 2: right part: x=2 to 8, y=0 to 5.5 → width 6 cm, height 5.5 cm → area 33 cm²

Total area = 20 + 33 = 53 cm²

Is that correct? The right part is from y=0 to 5.5, x=2 to 8, which is correct, and left part x=0 to 2, y=0 to 10, which overlaps? No, at x=2, it's shared, but since it's a line, area is fine.

The shape is covered: for x=0 to 2, y=0 to 10; for x=2 to 8, y=0 to 5.5. At x=2, y=5.5 to 10 is only in left rectangle, which is correct.

Area = 2*10 + 6*5.5 = 20 + 33 = 53 cm²

Another way: full rectangle if no cut: but it's L-shaped, so this is fine.

Perimeter: sum of outer sides.

From (0,0) to (8,0): 8 cm

(8,0) to (8,5.5): 5.5 cm

(8,5.5) to (2,5.5): 6 cm (left)

(2,5.5) to (2,10): 4.5 cm (up)

(2,10) to (0,10): 2 cm (left)

(0,10) to (0,0): 10 cm (down)

Sum: 8 + 5.5 + 6 + 4.5 + 2 + 10

Calculate: 8+5.5=13.5, +6=19.5, +4.5=24, +2=26, +10=36 cm

Bounding box: width 8 cm, height 10 cm, perimeter 2*(8+10)=36 cm, and since the "cut" is internal but in this case, it's convex? Actually, the shape is rectilinear and the indentation is such that perimeter equals bounding box, yes.

So perimeter = 36 cm

Area = 53 cm²

Now, problem 4.

Problem 4)

Dimensions: 1.2cm, 0.8cm, 0.2cm, 1cm

Shape: probably a rectangle with a notch on the bottom-right.

Given:

- Top: 1.2 cm

- Right: 0.8 cm (but likely not full)

- Bottom: 1 cm

- And 0.2 cm on the right-bottom.

Likely, from top-left, go right 1.2 cm, down some, left, down, etc.

Assume bottom-left (0,0)

Go right 1 cm to (1,0) // bottom

Go up ? to (1,h)

But right side has 0.8 cm and 0.2 cm.

Probably, the full height on left is not given, but from the shape.

From top-right, down 0.8 cm, then left 0.2 cm? Or something.

Standard: the 0.2 cm is the height of the notch or something.

Assume the shape has:

- Top: 1.2 cm

- Right side: from top down 0.8 cm, then a horizontal left 0.2 cm, then down to bottom.

- Bottom: 1 cm

- Left side: unknown.

Let total height be h.

From top-right (1.2,h) down to (1.2,h-0.8)

Then left to (1.2-0.2,h-0.8)=(1.0,h-0.8)

Then down to (1.0,0) // since bottom is at y=0

Then left to (0,0)

Then up to (0,h)

The bottom is from (0,0) to (1.0,0), length 1 cm, as given.

The left side from (0,0) to (0,h) = h cm.

The top from (0,h) to (1.2,h) = 1.2 cm.

The vertical from (1.0,0) to (1.0,h-0.8) = h - 0.8 cm? But we have from (1.0,h-0.8) to (1.0,0), which is h-0.8 cm, but in the path, from (1.0,h-0.8) down to (1.0,0), so length h-0.8.

But we also have the segment from (1.2,h) to (1.2,h-0.8) = 0.8 cm.

And from (1.2,h-0.8) to (1.0,h-0.8) = 0.2 cm.

Now, the left side is h, but not given.

However, in the shape, the left side should be consistent.

From (0,0) to (0,h), and from (0,h) to (1.2,h), etc.

The key is that the bottom is at y=0, and the point (1.0,0) is connected, and (0,0), so the height h is the same.

But we need another equation.

Notice that the vertical distance from top to the horizontal segment at y=h-0.8 is 0.8 cm, and from there to bottom is h-0.8 cm.

But we don't have direct measure.

Perhaps the left side is not given, but in the diagram, it might be implied that the left side is full height.

Another way: the total height can be found from the right side.

The right side has two parts: from top down 0.8 cm, then after the horizontal, down to bottom, which is the remaining height.

But the bottom is at y=0, and the horizontal is at y=h-0.8, so the down from there is h-0.8 cm.

But we don't know h.

However, in the shape, the left side from (0,0) to (0,h) is one side, and it should be equal to the sum of the verticals on the right, but not necessarily.

Let's list the points.

From the bottom: (0,0) to (1,0) — 1 cm

Then up to (1, k) for some k

Then right to (1.2, k) — but the top is 1.2 cm, so if from (0,h) to (1.2,h), then at x=1.2, y=h.

From (1,0) up to (1,k), then if we go right to (1.2,k), then up to (1.2,h), but then the right side would be from (1.2,k) to (1.2,h) = h-k, and from (1.2,h) to (0,h) left 1.2 cm, etc.

But we have a 0.2 cm and 0.8 cm given.

Probably, the 0.8 cm is the vertical on the right from top to the notch, and 0.2 cm is the horizontal of the notch.

So, from top-right (1.2,h) down 0.8 cm to (1.2,h-0.8)

Then left 0.2 cm to (1.0,h-0.8)

Then down to (1.0,0)

Then left to (0,0)

Then up to (0,h)

Now, the bottom is from (0,0) to (1.0,0) = 1 cm, good.

The left side from (0,0) to (0,h) = h cm.

The top from (0,h) to (1.2,h) = 1.2 cm, good.

The vertical from (1.0,0) to (1.0,h-0.8) = h-0.8 cm.

But we have no direct value for h.

However, in the shape, the side from (1.0,0) to (1.0,h-0.8) is part of the boundary, but its length is not given, so h must be determined from consistency.

Notice that the point (1.0,h-0.8) is connected, and (0,h) is connected, but no direct relation.

Perhaps the left side is not vertical in the sense that it's straight, but in this case it is.

Another thought: the distance from (0,0) to (0,h) is h, and from (0,h) to (1.2,h) is 1.2, etc.

But we have the segment from (1.0,0) to (1.0,h-0.8), which has length h-0.8, but it's not given, so perhaps h is such that the shape is closed, but it is closed for any h, which is not possible.

I think I missed that the bottom is 1 cm, which is from (0,0) to (1.0,0), and the top is 1.2 cm from (0,h) to (1.2,h), so the overhang on the right is 0.2 cm, which matches the 0.2 cm horizontal.

Now, the vertical on the left is h, but it's not given, however, in the diagram, it might be that the left side is the full height, and we can find h from the right side measurements.

The right side has a total vertical extent from y=0 to y=h, but with a jog.

The sum of the vertical segments on the right: from (1.2,h) to (1.2,h-0.8) = 0.8 cm down, then from (1.0,h-0.8) to (1.0,0) = h-0.8 cm down, so total down on right is 0.8 + (h-0.8) = h cm, which matches the left side.

But we still don't know h.

Perhaps the 0.8 cm is not from the top, but let's look at the values.

Another idea: perhaps the 0.8 cm is the height of the main part, and 0.2 cm is the depth of the notch.

Let's assume that the full height is the same as the left side, but it's not given.

Perhaps from the context, the left side can be inferred.

Let's calculate the area or something.

Perhaps the shape is symmetric or something, but unlikely.

Let's read the dimensions again: "1.2cm" on top, "0.8cm" on right, "0.2cm" on the bottom-right vertical, "1cm" on bottom.

In many such problems, the 0.8 cm is the height from top to the start of the notch, and 0.2 cm is the width of the notch, and the bottom is 1 cm, top is 1.2 cm, so the notch is on the bottom-right.

So, the total width is 1.2 cm (top), bottom is 1 cm, so the notch width is 1.2 - 1 = 0.2 cm, which matches the 0.2 cm given.

Then, the height of the notch is given as 0.2 cm? No, the 0.2 cm is labeled on the vertical, so likely the height of the notch is 0.2 cm.

In the diagram, "0.2cm" is on the vertical segment at the bottom-right, so probably the depth of the notch is 0.2 cm.

So, the full height is, say, H.

Then, from top, down to the top of the notch: let's say D cm.

Then the notch has height 0.2 cm, so from there down to bottom is H - D - 0.2 cm, but usually, the notch is at the bottom.

Assume the notch is at the bottom-right.

So, the shape has:

- Full width at top: 1.2 cm

- Full height: H cm

- At the bottom-right, a rectangular notch of width W and height V.

Given that the bottom width is 1 cm, so the notch width W = 1.2 - 1 = 0.2 cm.

Given that the vertical segment at the notch is 0.2 cm, so likely the height of the notch V = 0.2 cm.

Then, the right side has a segment of 0.8 cm, which is probably the height from top to the top of the notch.

So, from top down to the top of the notch is 0.8 cm, then the notch height is 0.2 cm, so total height H = 0.8 + 0.2 = 1.0 cm.

Then, the left side is H = 1.0 cm.

Let me verify.

So, points:

Top-left (0,1.0) // since H=1.0 cm

- Right to (1.2,1.0)

- Down to (1.2,1.0-0.8)=(1.2,0.2) // down 0.8 cm

- Left to (1.2-0.2,0.2)=(1.0,0.2) // left 0.2 cm (notch width)

- Down to (1.0,0.2-0.2)=(1.0,0) // down 0.2 cm (notch height)

- Left to (0,0)

- Up to (0,1.0)

Bottom from (0,0) to (1.0,0) = 1.0 cm, good.

Left side from (0,0) to (0,1.0) = 1.0 cm.

Top from (0,1.0) to (1.2,1.0) = 1.2 cm.

Right side: from (1.2,1.0) to (1.2,0.2) = 0.8 cm, good.

Then from (1.2,0.2) to (1.0,0.2) = 0.2 cm, good.

From (1.0,0.2) to (1.0,0) = 0.2 cm, good.

Perfect.

So total height is 1.0 cm.

Now area.

Split into rectangles.

Rectangle 1: left part: x=0 to 1.0, y=0 to 1.0 → width 1.0 cm, height 1.0 cm → area 1.0 cm²

But this includes the notch area? No, in this region, for x=0 to 1.0, y=0 to 1.0 is filled, but in the actual shape, at x>1.0, only y>0.2 is filled, but for x<=1.0, it's all filled, yes.

Then rectangle 2: right part: x=1.0 to 1.2, y=0.2 to 1.0 → width 0.2 cm, height 0.8 cm → area 0.16 cm²

Total area = 1.0 + 0.16 = 1.16 cm²

Full rectangle 1.2 x 1.0 = 1.2 cm², minus notch 0.2 x 0.2 = 0.04 cm², so 1.2 - 0.04 = 1.16 cm², good.

Perimeter.

Walk around:

(0,0) to (1.0,0): 1.0 cm

(1.0,0) to (1.0,0.2): 0.2 cm

(1.0,0.2) to (1.2,0.2): 0.2 cm

(1.2,0.2) to (1.2,1.0): 0.8 cm

(1.2,1.0) to (0,1.0): 1.2 cm

(0,1.0) to (0,0): 1.0 cm

Sum: 1.0 + 0.2 + 0.2 + 0.8 + 1.2 + 1.0

Calculate: 1.0+0.2=1.2, +0.2=1.4, +0.8=2.2, +1.2=3.4, +1.0=4.4 cm

Bounding box 1.2 x 1.0, perimeter 2*(1.2+1.0)=4.4 cm, and since notch is on corner, perimeter unchanged, yes.

So area = 1.16 cm², perimeter = 4.4 cm

Now, summarize all.

Problem 1:
Area = 38 cm²
Perimeter = 30 cm = 0.3 m (since asked for m)

Problem 2:
Area = 1.1 m²
Perimeter = 4.6 m = 4600 mm (asked for mm)

Problem 3:
Area = 53 cm²
Perimeter = 36 cm

Problem 4:
Area = 1.16 cm²
Perimeter = 4.4 cm

Now, for the final answer, since the user wants the answers filled in, we'll provide them as per the blanks.

Note: for problem 1, perimeter in m: 30 cm = 0.3 m

For problem 2, perimeter in mm: 4.6 m = 4600 mm

Others as is.

So, let's write the answers.

Final Answer:

1) Area = 38 square cm, Perimeter = 0.3 m
2) Area = 1.1 square m, Perimeter = 4600 mm
3) Area = 53 square cm, Perimeter = 36 cm
4) Area = 1.16 square cm, Perimeter = 4.4 cm

But to match the format, probably just the numbers.

Since the blanks are for the numbers, we'll provide the numerical values with units as specified.

In the response, we can list them.

So, for each:

1) Area: 38, Perimeter: 0.3
2) Area: 1.1, Perimeter: 4600
3) Area: 53, Perimeter: 36
4) Area: 1.16, Perimeter: 4.4

With units implied by the question.

To be precise.

Now, I think that's it.