Area of Compound Shapes (Composite Shapes) Worksheets - Free Printable

Let’s solve each compound shape one by one. We’ll break them into simpler shapes (like rectangles, triangles, semicircles), find their areas, and add or subtract as needed.

We’re told to use π = 3.14 and round answers to 2 decimal places if required.

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Shape 1:

This is a rectangle with a triangle on top and a triangle cut out from the bottom.

- Rectangle: width = 6 cm, height = 8 cm → Area = 6 × 8 = 48 cm²
- Top triangle: base = 6 cm, height = 5 cm → Area = (1/2) × 6 × 5 = 15 cm²
- Bottom triangle (cut out): base = 6 cm, height = 4 cm → Area = (1/2) × 6 × 4 = 12 cm²

Total area = rectangle + top triangle – bottom triangle
= 48 + 15 – 12 = 51.00 cm²

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Shape 2:

This looks like a trapezoid plus a rectangle on top? Wait — actually, it’s a large trapezoid with a small rectangle missing from the top right? Let me re-express:

Actually, better way: It’s a big trapezoid minus a small rectangle? Or maybe split into parts.

Looking again: The full shape can be seen as:

- A rectangle at the bottom: 10 m wide × 4 m high → Area = 10 × 4 = 40 m²
- A triangle on the left side: base = 6 m (since total height is 10 m, and rectangle is 4 m, so triangle height = 6 m), and base of triangle is 10 - 4 = 6 m? Wait, let's label properly.

Wait — dimensions given:

Left vertical side: 10 m
Bottom horizontal: 10 m
Top right has a step: 4 m up, then 4 m right? Actually, looking at the diagram description:

It says: left side 10 m, bottom 10 m, then there’s a part that goes up 4 m and right 4 m? Hmm.

Alternative approach: Think of it as a trapezoid with parallel sides 10 m and 4 m, height 10 m? No.

Wait — perhaps it’s composed of:

- A rectangle 4 m × 4 m on top right? But that doesn’t fit.

Better: Split vertically.

From left to right:

At x=0 to x=6: height is 10 m → rectangle 6×10 = 60? But no, because after x=6, it drops.

Actually, standard way for this shape:

It’s a trapezoid with bases 10 m and 4 m, and height 10 m? But the non-parallel sides are slanted.

Wait — look at coordinates mentally:

Start at bottom-left (0,0), go right 10 m to (10,0), up 4 m to (10,4), left 4 m to (6,4), up 6 m to (6,10), left 6 m to (0,10), down 10 m to (0,0). That makes sense.

So we can split into:

- Rectangle from x=0 to x=6, y=0 to y=10 → 6×10 = 60 m²
- Rectangle from x=6 to x=10, y=0 to y=4 → 4×4 = 16 m²

But wait — that would be overlapping? No, actually, from x=6 to x=10, only up to y=4, and from x=0 to x=6, up to y=10. So yes, two rectangles.

Total area = 6×10 + 4×4 = 60 + 16 = 76.00 m²

Alternatively, you could see it as a big rectangle 10×10 = 100, minus a rectangle 4×6 = 24 (the missing part on top right), so 100 - 24 = 76. Same answer.

Good.

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Shape 3:

This is a rectangle with a triangle attached on the right.

Rectangle: 9 cm × 6 cm → Area = 54 cm²

Triangle: base = 6 cm (same as rectangle height), height = 4 cm → Area = (1/2) × 6 × 4 = 12 cm²

Total area = 54 + 12 = 66.00 cm²

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Shape 4:

This is a parallelogram with a semicircle attached on the right.

Parallelogram: base = 12 m, height = 6 m → Area = base × height = 12 × 6 = 72 m²

Semicircle: diameter = 6 m → radius = 3 m
Area of circle = πr² = 3.14 × 3² = 3.14 × 9 = 28.26
Semicircle = half of that = 14.13 m²

Total area = 72 + 14.13 = 86.13 m²

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Shape 5:

This is a rectangle with a semicircle on top.

Rectangle: 12 ft × 6 ft → Area = 72 ft²

Semicircle: diameter = 12 ft → radius = 6 ft
Area of circle = 3.14 × 6² = 3.14 × 36 = 113.04
Semicircle = 56.52 ft²

Total area = 72 + 56.52 = 128.52 ft²

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Shape 6:

This is a square with four triangles cut out from the corners? Or rather, it’s a star-like shape made by cutting triangles from a square.

Actually, looking at dimensions: outer square is 10 in × 10 in? But the inner shape is formed by connecting midpoints? Wait.

Dimensions given: from center to corner is 5 in? And the “arms” extend 5 in.

Actually, this shape is a square rotated 45 degrees inside another square? Or it’s an octagon? No.

Standard interpretation: This is a square with side length 10 in, but with four right triangles cut off from the corners. Each triangle has legs of 5 in.

Wait — the diagram shows: from each corner, a line goes inward 5 in along both axes, forming a smaller square in the middle? Actually, no.

Another way: The shape is composed of a central square and four triangles? Or it’s a single polygon.

Actually, common problem: This is a square of side 10 in, and from each corner, a right triangle with legs 5 in is removed.

So original square area = 10 × 10 = 100 in²

Each triangle: (1/2) × 5 × 5 = 12.5 in²

Four triangles: 4 × 12.5 = 50 in²

Remaining area = 100 - 50 = 50.00 in²

Yes, that matches typical problems.

Alternatively, the remaining shape is a square rotated 45 degrees with diagonal 10 in? Then side = 10/√2, area = (10/√2)^2 = 100/2 = 50. Same.

Perfect.

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Now, compiling all answers:

1. 51.00 cm²
2. 76.00 m²
3. 66.00 cm²
4. 86.13 m²
5. 128.52 ft²
6. 50.00 in²

All rounded to 2 decimal places where needed.

Final Answer:
1. 51.00
2. 76.00
3. 66.00
4. 86.13
5. 128.52
6. 50.00