Worksheets: Area & perimeter of irregular rectangular shapes ... - Free Printable

Let’s solve each problem one by one. We’ll find the perimeter and area for each rectangular shape.

Remember:
- Perimeter = add up all the sides (or use formula: 2 × length + 2 × width)
- Area = length × width

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Problem 1:

Rectangle with sides: 36 mm and 10 mm

Perimeter = 2 × (36 + 10) = 2 × 46 = 92 mm
Area = 36 × 10 = 360 mm²

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Problem 2:

This is an L-shaped figure made of two rectangles.

Break it into two parts:

Top rectangle: 13 mm wide, 8 mm high → Area = 13 × 8 = 104 mm²
Bottom rectangle: 9 mm wide, 15 mm high → Area = 9 × 15 = 135 mm²
Total area = 104 + 135 = 239 mm²

Now perimeter — trace around the outside:

Start from top left:
→ Right 13 mm
↓ Down 8 mm
→ Right 9 mm? Wait — no, look again.

Actually, let’s label the full outer edges.

The total height on the right side is 8 + 15 = 23 mm
The bottom part sticks out to the right — so the full width at bottom is 13 + 9 = 22 mm? Wait — no.

Wait — looking at the diagram:

It says:
Top rectangle: 13 mm (width), 8 mm (height)
Below that, a rectangle sticking out to the right: 9 mm (width), 15 mm (height)

But they share a vertical edge? Actually, the 9 mm is attached to the right side of the top rectangle? Or below?

Looking at standard interpretation: It's like a step down to the right.

So overall shape:

Left side: 8 + 15 = 23 mm tall
Bottom: 13 + 9 = 22 mm wide? But wait — the 9 mm is only the extra part.

Actually, better to count all outer sides:

Top: 13 mm
Right side of top part: 8 mm
Then right side of bottom part: 15 mm
Bottom: 9 mm (the protruding part)
Then left along bottom of top part? No — we need to go back.

Actually, let’s list all outer edges in order:

Start at top-left corner:

1. Go right: 13 mm
2. Go down: 8 mm
3. Go right: 9 mm ← this is the “step”
4. Go down: 15 mm
5. Go left: 9 + 13 = 22 mm? Wait — no, because the bottom of the whole shape is only under the 9 mm part? That doesn’t make sense.

Wait — perhaps the 9 mm is the width of the lower rectangle, and it’s aligned to the right? So the total width at bottom is 13 + 9 = 22 mm? But then the left side would be straight?

Actually, re-examining: The diagram likely shows:

- A rectangle 13mm x 8mm on top left
- Attached to its bottom-right, another rectangle 9mm x 15mm going down and right

So the full shape has:

Outer perimeter:

Top: 13 mm
Right side of top rect: 8 mm
Then right side of bottom rect: 15 mm
Bottom: 9 mm
Then left along the bottom of the top rect? But there’s a gap.

Actually, after going down 15 mm on the right, you go left 9 mm (bottom of lower rect), then up 15 mm? No — that would be inside.

I think I’m overcomplicating. Let me draw mentally:

Imagine coordinates:

Top-left corner at (0,0)

Top rectangle: from (0,0) to (13,8) — so goes right 13, down 8

Then lower rectangle starts at (13,8) and goes right 9 and down 15 → so to (22,23)

So the full shape has corners at:

(0,0) → (13,0) → (13,8) → (22,8) → (22,23) → (0,23)? No — that’s not right.

Wait — if the lower rectangle is attached to the bottom of the top one, but shifted right, then the left side of the lower rectangle is at x=13, y=8 to y=23.

So the full outline:

Start at (0,0):

→ Right to (13,0) — top edge
↓ Down to (13,8) — right edge of top rect
→ Right to (22,8) — top edge of lower rect
↓ Down to (22,23) — right edge of lower rect
← Left to (0,23)? No — because from (22,23) we need to go left to where? The bottom of the shape is only under the lower rect? But what about under the top rect?

Actually, the bottom of the top rect is at y=8, from x=0 to x=13. The lower rect is from x=13 to x=22, y=8 to y=23. So the space from x=0 to x=13, y=8 to y=23 is empty? Then the left side of the shape is from (0,0) down to (0,8)? But then how do we connect to the bottom?

I think I have it wrong. Perhaps the lower rectangle is attached directly below the top one, but wider? The diagram says "9 mm" next to the lower part — probably meaning the width of the lower rectangle is 9 mm, and it's centered or something? But that doesn't help.

Alternative approach: In such problems, often the "L-shape" has known dimensions, and we can calculate perimeter by adding all outer sides.

Let me assume the following based on common textbook problems:

The shape consists of:

- A vertical rectangle on the left: 13 mm wide, 8+15=23 mm high? No.

Looking back at the image description: It says "13 mm" on top, "8 mm" on the right of top part, "9 mm" on the right of bottom part, "15 mm" on the bottom right.

Perhaps it's:

Total height on left: 8 + 15 = 23 mm
Total width at bottom: 13 + 9 = 22 mm? But then the top is only 13 mm.

Standard way: For an L-shape like this, perimeter is calculated by tracing the outer path.

Let me define the points:

Assume the top-left corner is A.

From A, go right 13 mm to B.
From B, go down 8 mm to C.
From C, go right 9 mm to D.
From D, go down 15 mm to E.
From E, go left 9 + 13 = 22 mm to F? But F should be directly below A.

If from E we go left 22 mm, we reach a point G which is 22 mm left of E. Since E is at (22,23) if A is (0,0), then G is at (0,23). Then from G go up 23 mm to A.

But is that correct? From E (22,23) to G (0,23) is left 22 mm, then up to (0,0) is 23 mm.

But in this case, the side from G to A is 23 mm, which is the full left side.

And the bottom from E to G is 22 mm.

Now, check if this matches the given dimensions.

In this path:

A to B: 13 mm (top)
B to C: 8 mm (right of top)
C to D: 9 mm (top of lower part)
D to E: 15 mm (right of lower part)
E to G: 22 mm (bottom) — but 22 = 13 + 9, yes
G to A: 23 mm (left side) — 23 = 8 + 15, yes

Perfect.

So perimeter = 13 + 8 + 9 + 15 + 22 + 23

Calculate: 13+8=21; 21+9=30; 30+15=45; 45+22=67; 67+23=90 mm

Area: as before, top rect 13×8=104, lower rect 9×15=135, total 239 mm²

But is the lower rect 9x15? In my coordinate, from C(13,8) to D(22,8) to E(22,23) to say H(13,23) — so yes, width 9, height 15.

And top rect from A(0,0) to B(13,0) to C(13,8) to I(0,8) — so 13x8.

No overlap, so area sum is fine.

So for problem 2:

Perimeter = 90 mm
Area = 239 mm²

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Problem 3:

Rectangle: 41 m by 24 m

Perimeter = 2 × (41 + 24) = 2 × 65 = 130 m
Area = 41 × 24

Calculate 40×24=960, 1×24=24, total 984 m²

Or 41×20=820, 41×4=164, 820+164=984 m²

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Problem 4:

Another L-shape.

Given: left part 15 cm high, bottom part 38 cm wide, right part 9 cm high, and 15 cm on the right bottom.

Similar to problem 2.

Assume:

Top-left to top-right: ? Not given directly.

From diagram description: "15 cm" on left, "9 cm" on right top, "38 cm" on bottom, "15 cm" on right bottom.

Probably:

The shape has a left rectangle 15 cm high, and a bottom rectangle extending right.

Assume the full width at bottom is 38 cm.

The right part has a "step": from bottom, up 15 cm, then left?

Standard interpretation:

- The left side is 15 cm high.
- The bottom is 38 cm wide.
- On the right, there is a part that goes up 9 cm, and then the remaining height is filled?

Perhaps it's symmetric to problem 2.

Let me define:

Start at top-left A.

Go right to B — distance? Not given.

From the labels: "15 cm" is on the left side, so height of left part is 15 cm.

"9 cm" is on the right side of the top part — so perhaps the top part has height 9 cm on the right.

"38 cm" is the total bottom width.

"15 cm" is on the right bottom — probably the height of the right-bottom rectangle.

So likely:

The shape is composed of:

- A top rectangle: width W, height 9 cm
- A bottom rectangle: width 38 cm, height 15 cm
But they overlap or are connected.

If the bottom rectangle is 38 cm wide and 15 cm high, and the top rectangle is sitting on top of it, but only covering part.

The "15 cm" on left suggests that on the left, the total height is 15 cm, which might mean the top rectangle is not present on the left? Confusing.

Another way: in many such problems, the L-shape has:

Vertical leg: height H, width W1
Horizontal leg: length L, height H2

Here, from the numbers: left side 15 cm, so perhaps the vertical part is 15 cm high.

Bottom 38 cm wide.

On the right, it says "9 cm" and "15 cm" — probably the horizontal part has height 9 cm, and the vertical part on right has height 15 cm, but that doesn't add up.

Perhaps the total height on left is 15 cm, on right is 9 cm, and the difference is made up by the bottom part.

Let's think of the outer perimeter.

Assume the shape looks like a backwards L or something.

From common problems, often:

The full height on left is 15 cm.

The full width at bottom is 38 cm.

On the right, there is a section that is 9 cm high, and below it 15 cm high, but that would make total height 24 cm on right, which contradicts left being 15 cm.

Unless the 15 cm on left is only part of it.

I recall that in some diagrams, for an L-shape, the dimensions are given for the arms.

Let me try this: suppose the vertical arm is 15 cm high and X cm wide, and the horizontal arm is Y cm long and 9 cm high, and they share a corner.

But we have "38 cm" on bottom, which is likely the total width.

Also, "15 cm" on the right bottom — perhaps the height of the horizontal arm is 15 cm? But it says "9 cm" on top right.

Perhaps "9 cm" is the height of the top part on the right, and "15 cm" is the height of the bottom part on the right, but then total height on right is 24 cm, while on left it's 15 cm, so the shape is not aligned.

This is messy. Let's look for a different approach.

In problem 2, we had a similar thing, and we used the fact that the total height and width can be inferred.

For problem 4, let's assume:

- The left side is 15 cm high.
- The bottom is 38 cm wide.
- The right side has a "notch": from the bottom, up 15 cm, then left for some distance, then up 9 cm to the top.

But then the top would be at height 15 + 9 = 24 cm on the right, but on left it's only 15 cm, so the top is slanted? No, it's rectilinear.

Perhaps the 15 cm on left is the height of the left rectangle, and the 9 cm is the height of the right rectangle, and they are at different levels.

Another idea: perhaps the shape is like a rectangle with a bite taken out, but usually it's additive.

Let's read the diagram description again: "15 cm" on left, "9 cm" on right top, "38 cm" on bottom, "15 cm" on right bottom.

Perhaps "15 cm" on right bottom means the width of the right-bottom part is 15 cm, but that doesn't make sense with "38 cm" on bottom.

I think I found a better way: in many textbooks, for such an L-shape, the dimensions are:

- The vertical part: height 15 cm, width A
- The horizontal part: length B, height 9 cm
- And the total width is 38 cm, which is A + B or something.

But we have "15 cm" on the right bottom — perhaps that's the height of the horizontal part.

Assume that the horizontal arm has height 15 cm, and the vertical arm has height 9 cm, but then the left side is labeled 15 cm, which might be the height of the vertical arm.

This is confusing. Let's try to search for a standard interpretation.

Perhaps the "15 cm" on left is the full height, "9 cm" on right is the height of the top part, so the bottom part on right has height 15 - 9 = 6 cm? But it says "15 cm" on right bottom, which might be the width.

I recall that in some problems, the number on the side indicates the length of that segment.

So for problem 4:

- Left side: 15 cm (vertical)
- Top-right side: 9 cm (vertical) — so from top, down 9 cm on the right
- Bottom: 38 cm (horizontal)
- Right-bottom side: 15 cm (horizontal) — so from right, left 15 cm on the bottom

Then, the shape has:

Start at top-left A.

Go right to B — distance unknown yet.
Go down to C — 9 cm (since "9 cm" on right top)
Go right to D — distance?
Go down to E — but we have "15 cm" on right bottom, which might be horizontal.

Perhaps "15 cm" on right bottom is the length of the bottom-right horizontal segment.

Assume:

From A (top-left), go right to B.
From B, go down 9 cm to C.
From C, go right to D.
From D, go down to E — but how far?
From E, go left 15 cm to F (since "15 cm" on right bottom)
From F, go left to G — but G should be below A.
From G, go up to A — 15 cm (left side).

Also, the bottom from E to F is 15 cm, and from F to G is some distance, and total bottom is 38 cm, so from E to G is 38 cm, so from F to G is 38 - 15 = 23 cm.

Then, the left side from G to A is 15 cm.

Now, the height from A to G is 15 cm, but from A to C is 9 cm down, then from C to E is additional down.

From C to E: since from E to G is up 15 cm? No, from G to A is up 15 cm, so the y-coordinate of G is 0 if A is at y=15, but let's set coordinates.

Set A at (0,15) — so y increases down or up? Usually in math, y increases up, but in geometry problems, sometimes down. To avoid confusion, let's use distances.

From A to G is 15 cm down (left side).

From G to F is 23 cm right (since total bottom 38 cm, and F to E is 15 cm, so G to F is 38 - 15 = 23 cm? No.

If from E to F is 15 cm left, and F to G is further left, and G to A is up, then the bottom is from E to G.

If E to F is 15 cm, and F to G is X cm, then E to G is 15 + X = 38 cm, so X = 23 cm.

So G to F is 23 cm right? Let's define directions.

Start at A (top-left).

Move right to B: let's call this distance P.
Move down to C: 9 cm.
Move right to D: distance Q.
Move down to E: distance R.
Move left to F: 15 cm (given as "15 cm" on right bottom).
Move left to G: distance S.
Move up to A: 15 cm (left side).

Also, the total bottom width from E to G is 38 cm, and since from E to F is 15 cm left, and F to G is S cm left, so 15 + S = 38, thus S = 23 cm.

Now, the left side from G to A is 15 cm up.

The height from A to E: from A down to C is 9 cm, then C to E is R cm down, so total down from A to E is 9 + R.

But from E to G is left 38 cm, and G to A is up 15 cm, so the net displacement from E to A is left 38 cm and up 15 cm, but in terms of path, we have to go via F and G.

For the shape to close, the vertical distance from A to E must equal the vertical distance from G to A minus something, but it's complicated.

Notice that from A to G is directly down 15 cm (left side).

From A to E: down 9 cm to C, then down R cm to E, so total down 9 + R cm.

From E to G: left 38 cm, and since G is at the same level as A? No, G is below A by 15 cm, and E is below A by 9 + R cm, so for G and E to be at the same y-level, we need 9 + R = 15, so R = 6 cm.

Yes! That makes sense.

So the down from C to E is 6 cm.

Then, the horizontal distances: from A to B is P, B to C is down, C to D is Q, D to E is down 6 cm.

From E to F is left 15 cm, F to G is left 23 cm (since 15+23=38), G to A is up 15 cm.

Now, for the shape to be closed, the horizontal position: from A to B to C to D to E, the x-coordinate of E should be the same as G, which is 0 if A is at x=0.

A at x=0.

B at x=P.

C at x=P.

D at x=P+Q.

E at x=P+Q.

F at x=P+Q - 15 (since left 15 cm).

G at x=P+Q - 15 - 23 = P+Q - 38.

But G should be at x=0, since directly below A.

So P+Q - 38 = 0, thus P+Q = 38.

Also, the top from A to B is P, and from B to C is down, then C to D is Q, so the top edge is only from A to B, length P.

The bottom from E to G is 38 cm, as given.

Now, we have P + Q = 38, but we don't know P and Q separately. However, for perimeter, we may not need them individually.

Let's list all sides for perimeter:

1. A to B: P cm (right)
2. B to C: 9 cm (down)
3. C to D: Q cm (right)
4. D to E: 6 cm (down) — since R=6
5. E to F: 15 cm (left)
6. F to G: 23 cm (left)
7. G to A: 15 cm (up)

Sum: P + 9 + Q + 6 + 15 + 23 + 15

But P + Q = 38, so 38 + 9 + 6 + 15 + 23 + 15

Calculate: 38+9=47; 47+6=53; 53+15=68; 68+23=91; 91+15=106 cm

So perimeter = 106 cm

Now area: the shape can be seen as a large rectangle minus a small rectangle, or as two rectangles.

One way: the full rectangle from A to the bottom-right would be width 38 cm, height 15 cm, but there is a missing part on the top-right.

From the coordinates:

A(0,15), B(P,15), C(P,6), D(P+Q,6), E(P+Q,0), F(P+Q-15,0), G(0,0)

Since P+Q=38, E(38,0), F(23,0), G(0,0)

The shape is polygon A-B-C-D-E-F-G-A

To find area, we can split into rectangles.

For example, rectangle from x=0 to x=P, y=0 to y=15: area P*15

Plus rectangle from x=P to x=38, y=0 to y=6: area (38-P)*6

But 38-P = Q, since P+Q=38.

So area = P*15 + Q*6

But we don't know P and Q.

Notice that the area can also be calculated as the area under the path.

Since we have the coordinates, we can use shoelace formula, but that's advanced.

Another way: the shape is equivalent to a rectangle 38 cm by 15 cm minus a rectangle on the top-right.

The full rectangle would be from (0,0) to (38,15), area 38*15=570 cm²

But in our shape, from x=P to x=38, y=6 to y=15 is missing.

Because from C(P,6) to D(38,6) to say H(38,15) to B(P,15), but in our shape, we have from B to C down, then to D right, so the region above y=6 and right of x=P is not included; instead, we have only down to y=6.

In the full rectangle 38x15, the part that is cut out is from x=P to x=38, y=6 to y=15, which is a rectangle of width Q=38-P, height 9 cm (since 15-6=9).

Height from y=6 to y=15 is 9 cm, yes.

So area of cut-out = Q * 9

Thus area of shape = full rectangle - cut-out = 38*15 - Q*9

But Q = 38 - P, and we don't know P.

However, in the expression, we have area = P*15 + Q*6, and P+Q=38.

So area = 15P + 6Q = 15P + 6(38-P) = 15P + 228 - 6P = 9P + 228

Still depends on P.

But that can't be; the area should be determined by the given dimensions.

I think I made a mistake.

In the shape, the top is only from A to B, length P, and then from B down to C, then right to D, etc.

The area should be the same regardless of P, as long as P+Q=38, but that doesn't make sense because if P is large, the shape is different.

For example, if P=38, Q=0, then it's a rectangle 38x15, but then from B(38,15) down to C(38,6), then since Q=0, D is at (38,6), then down to E(38,0), then left to F(23,0), G(0,0), up to A(0,15). But then from E(38,0) to F(23,0) is left 15 cm, F to G(0,0) left 23 cm, G to A(0,15) up 15 cm. But the top is from A(0,15) to B(38,15), so it's a rectangle with a bite on the bottom-right? No, in this case, the shape includes from y=0 to y=15 for x=0 to 38, but then from E to F to G, it's cutting off the bottom-right corner? I'm confused.

Perhaps for the area, we can see that the shape consists of:

- A rectangle on the left: width P, height 15 cm
- A rectangle on the bottom-right: width Q, height 6 cm (since from y=0 to y=6)

And they are adjacent, so total area = P*15 + Q*6

With P+Q=38.

But without knowing P and Q, we can't determine area. That suggests that in the diagram, there must be more information, or perhaps the "15 cm" on left and "9 cm" on right imply that the top is flat or something.

Another possibility: perhaps the "15 cm" on left is the height, "9 cm" on right is the height of the top part, and the bottom is 38 cm, and the "15 cm" on right bottom is the width of the bottom part, but then the height of the bottom part is not given.

I recall that in some problems, the L-shape has the arms of equal width, but here it's not specified.

Let's look back at the user's image description. It says for problem 4: "15 cm" on left, "9 cm" on right top, "38 cm" on bottom, "15 cm" on right bottom.

Perhaps "15 cm" on right bottom means the height of the right-bottom rectangle is 15 cm, but that would conflict with the left side being 15 cm.

Unless the left side is not the full height.

Perhaps the 15 cm on left is the height of the left rectangle, and the 9 cm on right is the height of the right rectangle, and they are stacked, but then the bottom 38 cm is the total width, and the 15 cm on right bottom is redundant or something.

I think I need to assume that the shape is symmetric or standard.

Upon second thought, in many grade 5 worksheets, for such an L-shape, the dimensions are given such that the missing parts can be inferred.

For problem 4, let's assume that the vertical part on left is 15 cm high, and the horizontal part on bottom is 38 cm wide, and the "9 cm" is the height of the top part on the right, and "15 cm" is the width of the right part on the bottom, but then the height of the horizontal part is not given.

Perhaps the "15 cm" on right bottom is the height of the horizontal arm.

Let's try this: suppose the horizontal arm has height 15 cm, and the vertical arm has height 9 cm, but then the left side is labeled 15 cm, which might be the height of the vertical arm, so contradiction.

Another idea: perhaps the 15 cm on left is the full height, 9 cm on right is the height of the top section, so the bottom section on right has height 15 - 9 = 6 cm, and the 15 cm on right bottom is the width of the bottom section.

Then, the total width is 38 cm, which is the width of the left part plus the width of the right part.

Let W_left be the width of the left rectangle, W_right be the width of the right rectangle.

Then W_left + W_right = 38 cm.

The left rectangle is 15 cm high, W_left wide.

The right rectangle is 6 cm high (since 15-9=6), W_right wide, and it is at the bottom.

Then area = W_left * 15 + W_right * 6

Again, depends on W_left and W_right.

But for perimeter, we can calculate.

Perimeter: start at top-left.

Go right W_left cm.
Go down 9 cm (to the top of the right rectangle? No.

If the left rectangle is full height 15 cm, and the right rectangle is only 6 cm high at the bottom, then from the top-left, go right W_left cm to the top-right of left rectangle.
Then down 15 cm to bottom-left of left rectangle.
Then right W_right cm to bottom-right of right rectangle.
Then up 6 cm to top-right of right rectangle.
Then left W_right cm? No, to connect to the left.

From the top-right of right rectangle, which is at (W_left + W_right, 6) if A is (0,15), but y=0 at bottom.

Set A(0,15) top-left.

Left rectangle: to B(W_left,15), then to C(W_left,0), then to D(0,0)? No.

If the right rectangle is attached to the bottom-right of the left rectangle, then from C(W_left,0) go right to E(W_left + W_right,0), then up to F(W_left + W_right,6), then left to G(W_left,6), then up to B(W_left,15)? But then from G to B is up 9 cm, which matches the "9 cm" on right top.

Yes!

So the shape is:

- Left rectangle: from (0,0) to (W_left,15) — but usually we think of y increasing down, but let's keep y increasing up for consistency, or switch.

To make it easy, let's say y=0 at bottom.

So A(0,15) top-left.

B(W_left,15) top-right of left rect.

C(W_left,0) bottom-right of left rect.

D(W_left + W_right,0) bottom-right of right rect.

E(W_left + W_right,6) top-right of right rect.

F(W_left,6) top-left of right rect.

Then from F to B is up 9 cm (since 15-6=9), which matches "9 cm" on right top.

From D to E is up 6 cm, but not labeled.

From C to D is right W_right cm.

From E to F is left W_right cm.

From F to B is up 9 cm.

From B to A is left W_left cm.

From A to say H(0,0) down 15 cm, but in this case, from A to C is not direct; we have to go A to B to C, but C is at (W_left,0), and A is at (0,15), so to close, from C to (0,0) is left W_left cm, then up to A 15 cm.

In the shape, the bottom is from (0,0) to (W_left + W_right,0), so from C(W_left,0) to D(W_left + W_right,0) is right W_right cm, and from (0,0) to C(W_left,0) is right W_left cm, but (0,0) is not yet connected.

So the vertices are: A(0,15), B(W_left,15), C(W_left,0), D(W_left + W_right,0), E(W_left + W_right,6), F(W_left,6), then back to B? But B is already visited.

From F(W_left,6) to B(W_left,15) is up 9 cm, but B is already in the path.

The correct path for perimeter: start at A(0,15).

Go right to B(W_left,15).
Go down to C(W_left,0).
Go right to D(W_left + W_right,0).
Go up to E(W_left + W_right,6).
Go left to F(W_left,6).
Go up to B(W_left,15)? But B is already visited, and we would be double-counting.

From F(W_left,6) , we should go to A(0,15)? But that's diagonal.

I think the shape is not convex, and the path should be A-B-C-D-E-F- then to a point below A.

From F(W_left,6) , if we go left to G(0,6), then up to A(0,15).

Yes! That makes sense.

So add G(0,6).

Then the path: A(0,15) -> B(W_left,15) -> C(W_left,0) -> D(W_left + W_right,0) -> E(W_left + W_right,6) -> F(W_left,6) -> G(0,6) -> A(0,15)

Now, the segments:

A to B: W_left cm (right)
B to C: 15 cm (down)
C to D: W_right cm (right)
D to E: 6 cm (up)
E to F: W_right cm (left)
F to G: W_left cm (left) [since from x=W_left to x=0]
G to A: 9 cm (up) [from y=6 to y=15]

Also, the bottom from C to D is W_right, and from (0,0) to C is not directly, but in this path, from C to D is right, then later from F to G is left, but the bottom is only from C to D, and from (0,0) to C is not included because we have G at (0,6), not (0,0).

In this path, the point (0,0) is not visited; the bottom-left is at (0,6)? But that can't be, because the left side is from (0,6) to (0,15), 9 cm, but the problem says "15 cm" on left, which should be the full height.

In this case, from G(0,6) to A(0,15) is 9 cm, but the left side should be 15 cm, so perhaps G is at (0,0).

Let's set G at (0,0).

Then from F(W_left,6) to G(0,0)? Diagonal, not good.

From F(W_left,6) go left to H(0,6), then down to G(0,0), then right to C(W_left,0), but then we have overlap.

I think the correct way is that the left side is from (0,0) to (0,15), 15 cm.

Then from (0,15) to (W_left,15) .
From (W_left,15) to (W_left,6) — down 9 cm.
From (W_left,6) to (W_left + W_right,6) — right W_right cm.
From (W_left + W_right,6) to (W_left + W_right,0) — down 6 cm.
From (W_left + W_right,0) to (0,0) — left (W_left + W_right) cm.
From (0,0) to (0,15) — up 15 cm.

But then the bottom is from (0,0) to (W_left + W_right,0), length W_left + W_right = 38 cm, as given.

And the "15 cm" on right bottom — perhaps it's the width of the right part, but in this case, from (W_left,0) to (W_left + W_right,0) is W_right, and if "15 cm" is that, then W_right = 15 cm.

Similarly, "9 cm" on right top is the down from (W_left,15) to (W_left,6), which is 9 cm, good.

"15 cm" on left is from (0,0) to (0,15), good.

"38 cm" on bottom is from (0,0) to (38,0), so W_left + W_right = 38.

If W_right = 15 cm (from "15 cm" on right bottom), then W_left = 38 - 15 = 23 cm.

Perfect.

So now we have:

W_left = 23 cm
W_right = 15 cm

Now perimeter: list the sides:

1. (0,15) to (23,15): 23 cm right
2. (23,15) to (23,6): 9 cm down
3. (23,6) to (38,6): 15 cm right (since W_right=15)
4. (38,6) to (38,0): 6 cm down
5. (38,0) to (0,0): 38 cm left
6. (0,0) to (0,15): 15 cm up

Sum: 23 + 9 + 15 + 6 + 38 + 15

Calculate: 23+9=32; 32+15=47; 47+6=53; 53+38=91; 91+15=106 cm

Same as before.

Area: can be calculated as area of left rectangle plus area of right rectangle.

Left rectangle: from x=0 to 23, y=0 to 15: area 23*15 = 345 cm²

Right rectangle: from x=23 to 38, y=0 to 6: area 15*6 = 90 cm²

Total area = 345 + 90 = 435 cm²

As full rectangle 38*15 = 570 cm² minus the missing part: from x=23 to 38, y=6 to 15: width 15 cm, height 9 cm, area 135 cm², so 570 - 135 = 435 cm², same.

So for problem 4:

Perimeter = 106 cm
Area = 435 cm²

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Problem 5:

Rectangle: 36 m by 11 m

Perimeter = 2 × (36 + 11) = 2 × 47 = 94 m
Area = 36 × 11 = 396 m² (since 36*10=360, 36*1=36, total 396)

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Problem 6:

Rectangle: 20 m by 17 m

Perimeter = 2 × (20 + 17) = 2 × 37 = 74 m
Area = 20 × 17 = 340 m²

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Problem 7:

L-shape again.

Given: "12 mm" on top, "7 mm" on left, "6 mm" on right, "14 mm" on bottom.

Similar to previous.

Assume:

- Top: 12 mm
- Left: 7 mm
- Right: 6 mm
- Bottom: 14 mm

Probably, the shape has a top rectangle and a bottom rectangle.

Assume the left side is 7 mm high, right side is 6 mm high, so perhaps the bottom is lower on the right.

Or vice versa.

Commonly, for such a shape, it might be that the top is 12 mm wide, left side 7 mm high, then it steps down, and bottom is 14 mm wide, right side 6 mm high.

So likely, the full height on left is 7 mm, on right is 6 mm, so the difference is 1 mm, but that might not be.

Perhaps the 7 mm and 6 mm are heights of different parts.

Assume the shape is composed of two rectangles:

- Top rectangle: width 12 mm, height H1
- Bottom rectangle: width 14 mm, height H2

But they overlap or are connected.

From the dimensions, probably the left side is 7 mm, which might be the height of the left part, and right side 6 mm for the right part.

Suppose the top rectangle is 12 mm wide, and the bottom rectangle is 14 mm wide, and they are aligned on the left or right.

If aligned on the left, then the right side of the top is at x=12, bottom at x=14, so the bottom extends 2 mm to the right.

Then the height: if the left side is 7 mm, that might be the total height on left, so if the top rectangle has height A, bottom has height B, then A + B = 7 mm on left.

On the right, for the top rectangle, height A, for the bottom rectangle, height B, but since the bottom extends, on the right, from y=0 to y=B for the bottom, and from y=B to y=B+A for the top, but if the top is only up to x=12, then for x>12, only the bottom is there, so on the right side, at x=14, the height is B mm, and it's given as 6 mm, so B = 6 mm.

Then on left, A + B = 7, so A + 6 = 7, thus A = 1 mm.

Then the top rectangle is 12 mm wide, 1 mm high.

Bottom rectangle is 14 mm wide, 6 mm high.

They are aligned on the left, so the top is from x=0 to 12, y=6 to 7 (if y=0 at bottom), or y=0 to 1 for top, but let's set y=0 at bottom.

So bottom rectangle: x=0 to 14, y=0 to 6.

Top rectangle: x=0 to 12, y=6 to 7 (since A=1 mm).

Then the left side from (0,0) to (0,7) is 7 mm, good.

Right side: at x=14, from y=0 to y=6, so 6 mm, good.

Top: from (0,7) to (12,7), 12 mm, good.

Bottom: from (0,0) to (14,0), 14 mm, good.

Perfect.

So now perimeter: trace the outer path.

Start at (0,7) top-left.

Go right to (12,7): 12 mm
Go down to (12,6): 1 mm (since from y=7 to y=6)
Go right to (14,6): 2 mm (since 14-12=2)
Go down to (14,0): 6 mm
Go left to (0,0): 14 mm
Go up to (0,7): 7 mm

Sum: 12 + 1 + 2 + 6 + 14 + 7

Calculate: 12+1=13; 13+2=15; 15+6=21; 21+14=35; 35+7=42 mm

Area: top rect 12*1 = 12 mm²
Bottom rect 14*6 = 84 mm²
Total 96 mm²

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Problem 8:

Another L-shape.

Given: "10 m" on left, "6 m" on right top, "28 m" on bottom, "11 m" on right bottom.

Similar to problem 4.

Assume:

- Left side: 10 m high
- Right top: 6 m high — so perhaps the top part on right is 6 m high
- Bottom: 28 m wide
- Right bottom: 11 m — probably the width of the right-bottom part

Following the same logic as problem 4.

Assume the shape has:

- Left rectangle: width W_left, height 10 m
- Right rectangle: width W_right, height H_right

But from the dimensions, likely the right side has a step.

Assume that the full height on left is 10 m.

On the right, the top part is 6 m high, so the bottom part on right has height 10 - 6 = 4 m? But it says "6 m" on right top, and "11 m" on right bottom, which might be width.

In problem 4, we had "15 cm" on right bottom as width.

So here, "11 m" on right bottom is likely the width of the right-bottom rectangle.

Also, "6 m" on right top is the height of the top-right rectangle.

Then, the total bottom width is 28 m, which is W_left + W_right.

And the height on left is 10 m, which is the height of the left rectangle.

The right rectangle has height 6 m for the top part, but since it's at the top, and the bottom is lower, actually in the standard configuration, the right rectangle is at the bottom, with height H, and the top is only on the left.

From problem 4 analogy, in problem 4, we had the right rectangle at the bottom with height 6 cm, and width W_right=15 cm, and left rectangle height 15 cm, width W_left=23 cm, total width 38 cm.

Here, similarly, assume that the right-bottom rectangle has width 11 m (given as "11 m" on right bottom), and height H_b.

The left rectangle has height 10 m, width W_left.

Total bottom width 28 m = W_left + 11, so W_left = 28 - 11 = 17 m.

Now, the height: on the right, the "6 m" on right top — in problem 4, we had "9 cm" on right top, which was the height from the top of the right rectangle to the top of the left rectangle.

In problem 4, left rectangle height 15 cm, right rectangle height 6 cm, so the difference is 9 cm, which was the "9 cm" on right top.

Here, left rectangle height 10 m, right rectangle height H_b, so the difference is 10 - H_b, and this should be the "6 m" on right top.

So 10 - H_b = 6, thus H_b = 4 m.

So right rectangle is 11 m wide, 4 m high.

Left rectangle is 17 m wide, 10 m high.

Aligned on the left.

So coordinates: A(0,10) top-left.

B(17,10) top-right of left rect.

C(17,0) bottom-right of left rect.

D(28,0) bottom-right of right rect (since 17+11=28).

E(28,4) top-right of right rect.

F(17,4) top-left of right rect.

Then from F to B is up 6 m (10-4=6), good.

Perimeter path: A(0,10) -> B(17,10) -> C(17,0) -> D(28,0) -> E(28,4) -> F(17,4) -> G(0,4) -> A(0,10)? But G(0,4) to A(0,10) is up 6 m, but the left side should be 10 m from (0,0) to (0,10).

Mistake.

In this setup, the bottom-left is at (0,0), but in the path, from C(17,0) to D(28,0), then to E(28,4), etc., but (0,0) is not connected directly.

To include (0,0), we need to go from C(17,0) to (0,0) left 17 m, then up to A(0,10) 10 m, but then we miss the right part.

Correct path for the shape described:

The shape includes:

- From (0,0) to (17,0) to (17,10) to (0,10) for left rectangle, but then the right rectangle is from (17,0) to (28,0) to (28,4) to (17,4), so the full shape has a "notch" or something.

Actually, the union is from x=0 to 28, but with a cut.

Specifically, for x from 0 to 17, y from 0 to 10; for x from 17 to 28, y from 0 to 4.

So the boundary:

Start at (0,10).

Go right to (17,10).
Go down to (17,4). // because at x=17, from y=10 to y=4 is the edge between left and right, but in the shape, at x=17, for y>4, it's only left rectangle, for y<4, both, but the edge is internal.

For perimeter, we go around the outside.

So from (0,10) to (17,10) : 17 m right
Then from (17,10) down to (17,4) : 6 m down (since 10-4=6)
Then from (17,4) right to (28,4) : 11 m right
Then from (28,4) down to (28,0) : 4 m down
Then from (28,0) left to (0,0) : 28 m left
Then from (0,0) up to (0,10) : 10 m up

Sum: 17 + 6 + 11 + 4 + 28 + 10

Calculate: 17+6=23; 23+11=34; 34+4=38; 38+28=66; 66+10=76 m

Area: left rect 17*10 = 170 m²
Right rect 11*4 = 44 m²
Total 214 m²

Full rectangle 28*10=280 m² minus the missing part: from x=17 to 28, y=4 to 10: width 11 m, height 6 m, area 66 m², so 280-66=214 m², good.

So for problem 8:

Perimeter = 76 m
Area = 214 m²

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Now, summarize all answers:

1. Perimeter: 92 mm, Area: 360 mm²
2. Perimeter: 90 mm, Area: 239 mm²
3. Perimeter: 130 m, Area: 984 m²
4. Perimeter: 106 cm, Area: 435 cm²
5. Perimeter: 94 m, Area: 396 m²
6. Perimeter: 74 m, Area: 340 m²
7. Perimeter: 42 mm, Area: 96 mm²
8. Perimeter: 76 m, Area: 214 m²

Final Answer:
1. Perimeter: 92 mm, Area: 360 mm²
2. Perimeter: 90 mm, Area: 239 mm²
3. Perimeter: 130 m, Area: 984 m²
4. Perimeter: 106 cm, Area: 435 cm²
5. Perimeter: 94 m, Area: 396 m²
6. Perimeter: 74 m, Area: 340 m²
7. Perimeter: 42 mm, Area: 96 mm²
8. Perimeter: 76 m, Area: 214 m²