Area of Composite Shapes — Printable Math Worksheet - Free Printable

Let’s solve this step by step.

We are told to color all composite shapes with an area greater than 40.

A “composite shape” is made of two or more simple shapes (like rectangles) stuck together. To find the total area, we break each shape into rectangles, calculate each rectangle’s area (length × width), then add them up.

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Shape 1 (top center):

It looks like a big rectangle with a smaller rectangle sticking out on the right.

Break it into:
- Left part: width = 5, height = 7 → area = 5 × 7 = 35
- Right part: width = 3, height = 4 → area = 3 × 4 = 12

Total area = 35 + 12 = 47

→ 47 > 40 → ✔ Color this one.

Wait — let me double-check the dimensions.

Actually, looking again: The left side is 7 tall and 5 wide. Then on the top right, there’s a bump that sticks out 3 units wide and 4 units high? But wait — if the full height on the left is 7, and the right part is only 4 tall, then maybe the bottom part extends under both?

Alternative way: Think of it as one big rectangle minus a missing piece? Or better — split horizontally.

Actually, here's a better breakdown:

The entire shape can be seen as:
- A large rectangle at the bottom: width = 5 + 3 = 8, height = 4 → area = 8 × 4 = 32
- Plus a small rectangle on top left: width = 5, height = 7 - 4 = 3 → area = 5 × 3 = 15

Total = 32 + 15 = 47 → same as before.

✔ Still 47 > 40 → color it.

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Shape 2 (middle left): Two squares/rectangles side by side

Left: 5 × 5 = 25
Right: 4 × 4 = 16
Total = 25 + 16 = 41

→ 41 > 40 → ✔ Color this one.

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Shape 3 (middle right): L-shaped or stepped shape

Break into two parts:

Option 1:
- Bottom rectangle: width = ? Let’s see — the vertical sides are labeled 4 and 5. The top has segments 2 and 3.

Actually, think of it as:
- Left column: width = 2, height = 4 → area = 8
- Right column: width = 3, height = 5 → area = 15
But they overlap? No — actually, the shape is connected.

Better approach: Imagine the full bounding box.

Total width = 2 + 3 = 5
Total height = 5 (on the right)

But the left side only goes up to 4, so there’s a notch.

So: Area = (full rectangle 5×5) minus the missing top-left corner.

Missing part: width = 2, height = 5 - 4 = 1 → area = 2×1 = 2

Full rectangle: 5×5 = 25
Minus 2 → 23? That seems too small.

Wait — no, that doesn’t match the labels.

Let me label coordinates mentally.

From left to right: first segment width 2, then 3 → total width 5.

Height on left is 4, on right is 5.

So the shape has:
- A rectangle on the left: 2 wide × 4 high = 8
- A rectangle on the right: 3 wide × 5 high = 15
But do they share a base? Yes — so total area = 8 + 15 = 23? That can’t be right because 23 < 40, but let’s verify.

Wait — actually, when you put them side by side, the left part is only 4 tall, and the right part is 5 tall, so yes — no overlap, just adjacent. So total area = 2×4 + 3×5 = 8 + 15 = 23

But 23 is less than 40 → ✘ Do NOT color.

Wait — I think I misread the diagram.

Looking again: The shape has a "step" — the top edge goes right 2, then down, then right 3? Actually, standard interpretation:

This is a single polygon. Let’s use the method of dividing into horizontal strips.

Bottom strip: full width = 2 + 3 = 5, height = 4 → area = 5×4 = 20
Top strip: only over the right part, width = 3, height = 5 - 4 = 1 → area = 3×1 = 3
Total = 20 + 3 = 23

Same result.

Alternatively, vertical strips:
Left: 2×4 = 8
Right: 3×5 = 15
Total = 23

Yes. So area = 23 → not greater than 40 → skip.

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Shape 4 (bottom): Two rectangles side by side

Left: 12 × 3 = 36
Right: 3 × 3 = 9
Total = 36 + 9 = 45

→ 45 > 40 → ✔ Color this one.

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Now summarize:

- Shape 1: 47 → color
- Shape 2: 41 → color
- Shape 3: 23 → don’t color
- Shape 4: 45 → color

So three shapes should be colored: top center, middle left, and bottom.

Final Answer:
Color the top-center shape, the middle-left shape, and the bottom shape.