Math worksheet for calculating the area of composite shapes.

Let’s solve each problem step by step. We’ll break the composite shapes into simpler parts (like rectangles and triangles), find their areas, then add them up.

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Problem 1:

This shape looks like a big rectangle with two smaller rectangles cut out from the top.

But actually, it’s easier to think of it as:

- A large bottom rectangle that is 13m long and... how tall? The total height on the left is 10m, and there’s a 5m section at the top, so the bottom part must be 10m - 5m = 5m tall.
→ So bottom rectangle: 13m × 5m = 65 m²

Now look at the top part — it has two separate blocks:
- Left block: 5m wide × 5m tall = 25 m²
- Right block: 5m wide × 5m tall = 25 m²

Wait — but between them there’s a gap of 3m. Let’s check if the widths add up:

Left block (5m) + gap (3m) + right block (5m) = 13m → matches the bottom width. Good.

So total area = bottom rectangle + left top + right top
= 65 + 25 + 25 = 115 m²

✔ Double-check: Another way — imagine the whole thing as a 13m × 10m rectangle = 130 m², then subtract the missing middle part (which is 3m wide × 5m tall = 15 m²).
130 - 15 = 115 m² → same answer!

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Problem 2:

This shape is made of a rectangle and a triangle attached to its right side.

Rectangle: 9cm long × 8cm tall = 72 cm²

Triangle: base = 8cm (same as rectangle’s height), height = 6cm (given by dashed line)

Area of triangle = (base × height) ÷ 2 = (8 × 6) ÷ 2 = 48 ÷ 2 = 24 cm²

Total area = 72 + 24 = 96 cm²

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Problem 3:

This is an L-shaped figure. We can split it into two rectangles.

Option 1: Split vertically.

- Left rectangle: 4m wide × 6m tall = 24 m²
- Bottom rectangle: extends to the right. Total length is 10m, we already used 4m on the left, so this part is 10 - 4 = 6m long. Height? The vertical part was 6m, but the horizontal arm is only 5m high? Wait — let’s read carefully.

Actually, looking at the labels:

The full left side is 6m tall. The inner corner says “5m” — that’s the height of the right part of the L.

So better to split horizontally:

Top rectangle: 4m wide × ? tall. The total height is 6m, and the lower part is 5m? That doesn’t make sense.

Wait — let’s re-read the diagram description:

It says:

- Left side: 6m (full height)
- Top horizontal: 4m
- Then down 5m (so from top, going down 5m, meaning the remaining height below that is 6 - 5 = 1m?)
- Then rightward to make total bottom length 10m.

Actually, standard way for L-shape:

Split into two rectangles:

Rectangle A (vertical part): 4m wide × 6m tall = 24 m²

Rectangle B (horizontal part sticking out): It starts after the 4m, so width = 10 - 4 = 6m. What’s its height? From the diagram, the drop-down is labeled 5m — that means from the top, you go down 5m before turning right. So the horizontal part is at the bottom, and its height is the remaining: 6m - 5m = 1m? But that seems too small.

Wait — maybe the 5m is the height of the horizontal leg? Let me reinterpret.

Looking again: The shape goes:

Start at bottom-left. Go up 6m. Go right 4m. Go down 5m. Go right ??? to make total bottom 10m. Then go down to close.

If you go up 6m, then right 4m, then down 5m — now you’re 1m above the bottom. Then you go right some distance, then down 1m to meet the bottom.

Total bottom length is 10m. You’ve already gone right 4m at the top, so the bottom extension must be 10 - 4 = 6m.

So the horizontal part at the bottom is 6m long and 1m tall? But the label says “5m” next to the vertical drop — that’s the 5m you went down from the top.

Actually, perhaps the 5m is the height of the right-side vertical segment? No.

Better approach: Use the outer dimensions.

Imagine the full rectangle if it weren’t L-shaped: 10m wide × 6m tall = 60 m²

Now, what’s missing? The top-right corner is cut out.

How big is the cut-out?

From the top: you have 4m covered on the left, so missing width = 10 - 4 = 6m

From the top down: you go down 5m before turning, so the cut-out starts at 5m down from top? Actually, no — when you go right 4m, then down 5m, that means the cut-out region is from x=4m to x=10m, and y=0 to y=1m? I’m getting confused.

Let me assign coordinates.

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

Go up to (0,6).
Go right to (4,6).
Go down to (4,1) — because you go down 5m from y=6 to y=1.
Then go right to (10,1).
Then down to (10,0).
Then left to (0,0).

So the shape consists of:

- Rectangle from (0,0) to (4,6): 4×6 = 24 m²
- Rectangle from (4,0) to (10,1): width=6m, height=1m → 6×1 = 6 m²

Total = 24 + 6 = 30 m²

But wait — is that correct? The label says “5m” next to the vertical drop — which is from y=6 to y=1, that’s 5m, yes. And bottom total is 10m, yes.

Alternatively, split differently:

Vertical rectangle on left: 4m × 6m = 24 m²
Horizontal rectangle at bottom: from x=0 to x=10, but only from y=0 to y=1? But that would include under the left part twice.

No — better to do:

The entire shape can be seen as:

- A 4m × 6m rectangle on the left
- Plus a 6m × 1m rectangle on the bottom right (since from x=4 to x=10 is 6m, and from y=0 to y=1 is 1m)

Yes, that avoids overlap.

So 24 + 6 = 30 m²

Another way: Full bounding box 10×6=60, minus the missing top-right rectangle: from x=4 to 10 (6m wide), and from y=1 to 6 (5m tall) → 6×5=30 m² missing? Then 60 - 30 = 30 m². Same answer!

Perfect.

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Final Answers:

1. 115 m²
2. 96 cm²
3. 30 m²

Final Answer:
1. 115 m²
2. 96 cm²
3. 30 m²