Math worksheet featuring six problems for calculating the area of compound shapes, including composite figures with semi-circles and polygons.

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

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

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Problem 1: Rectangle + Semicircle

Shape: A rectangle with a semicircle on the right side.

- Rectangle: length = 15 cm, width = 8 cm → Area = 15 × 8 = 120 cm²
- Semicircle: diameter = 8 cm → radius = 4 cm
Area of full circle = πr² = 3.14 × 4² = 3.14 × 16 = 50.24 cm²
So semicircle = 50.24 ÷ 2 = 25.12 cm²

Total area = 120 + 25.12 = 145.12 cm²

✔ Final Answer for #1: 145.12

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Problem 2: Trapezoid + Triangle? Wait — let’s look again.

Actually, this is a trapezoid on top of a rectangle? Or maybe it's a pentagon made from a rectangle and a triangle?

Wait — looking at dimensions:

Left vertical = 9 cm
Bottom horizontal = 20 cm
Top left slant goes up 7 cm over some base? Actually, better to split vertically.

Alternative approach: Split into a rectangle and a triangle on top.

But wait — the figure has:

- Left side: 9 cm tall
- Bottom: 20 cm wide
- Top part: starts at height 9 - 7 = 2 cm? No — actually, the “7” is labeled on the left upper segment.

Actually, re-examining: The shape looks like a trapezoid sitting on a rectangle? But no — perhaps it’s a rectangle with a triangle cut off? Let me think differently.

Better way: Divide the shape into two parts:

→ A rectangle at the bottom: height = 9 - 7 = 2 cm? That doesn’t make sense.

Wait — label says:

Vertical left side total = 9 cm
From bottom up 7 cm, then there’s a diagonal going to the top right corner.

Actually, this is a trapezoid with parallel sides: one is 20 cm (bottom), the other is... what’s the top?

The top horizontal part isn't given directly. But we can see that from the left, after rising 7 cm, it slopes to the right end which is at height 9 cm? That would mean the top is not horizontal.

Wait — perhaps it’s composed of:

- A rectangle: 20 cm wide × 2 cm high (since 9 - 7 = 2) → area = 40 cm²
- Plus a trapezoid on top? Or a triangle?

Actually, here’s a better breakdown:

Imagine drawing a vertical line down from the top-left corner of the sloped part. You get:

→ A rectangle on the left: width = ? Not given.

This is tricky without seeing exact labels. But standard interpretation for such figures:

It’s likely a rectangle plus a right triangle on top.

Assume:

- Bottom rectangle: 20 cm wide × 2 cm high → area = 40 cm²
- Above it, a right triangle: base = 20 cm, height = 7 cm → area = (1/2)*20*7 = 70 cm²

Wait — but then total height would be 2 + 7 = 9 cm — matches!

And the slope is the hypotenuse of the triangle.

Yes! So:

Area = rectangle + triangle = (20 × 2) + (½ × 20 × 7) = 40 + 70 = 110 cm²

✔ Final Answer for #2: 110.00

*(Note: Since no decimals needed, we write 110.00 to match format)*

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Problem 3: Hexagon-like shape — actually a rhombus? Or kite?

Given diagonals: one is 12 m, the other is 8 m.

For any quadrilateral with perpendicular diagonals (like a rhombus or kite), area = (d1 × d2)/2

So: (12 × 8)/2 = 96/2 = 48 m²

✔ Final Answer for #3: 48.00

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Problem 4: L-shaped figure — rectangle minus smaller rectangle

Outer rectangle: 12 ft × 8 ft = 96 ft²
Inner missing rectangle: (12 - 5) = 7 ft wide? Wait — let’s read carefully.

Label shows:

Total width = 12 ft
Height on left = 8 ft
On the right, there’s a notch: depth = 3 ft, and the remaining height on right is 8 - 3 = 5 ft? Wait — no.

Actually, the figure is an L-shape formed by:

- Big rectangle: 12 ft wide × 8 ft tall → 96 ft²
- Minus a small rectangle in the top-right corner: width = 5 ft, height = 3 ft → 15 ft²

Why? Because the inner cutout is 5 ft across and 3 ft down from top.

So area = 96 - 15 = 81 ft²

Alternatively, split into two rectangles:

→ Left rectangle: 7 ft wide × 8 ft tall = 56 ft²
→ Right rectangle: 5 ft wide × 5 ft tall = 25 ft²
Total = 56 + 25 = 81 ft² — same result.

✔ Final Answer for #4: 81.00

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Problem 5: Parallelogram + Rectangle? Or just a parallelogram?

Actually, it’s a parallelogram attached to a rectangle below? Wait — no.

Looking at labels:

Left side: 8 ft (vertical)
Bottom: 10 ft (horizontal)
Right side: also 8 ft? And top is slanted.

Actually, this is a parallelogram with base = 10 ft, height = 8 ft → area = base × height = 10 × 8 = 80 ft²

Wait — but why is there a "10" on the bottom and "8" on the side? In a parallelogram, area is base times perpendicular height.

If the 8 ft is the vertical height (which it appears to be, since it’s drawn straight up), then yes — area = 10 × 8 = 80 ft².

No need to complicate — it’s a standard parallelogram.

✔ Final Answer for #5: 80.00

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Problem 6: Triangle on top of a semicircle

Triangle: base = 10 in, height = 8 in → area = (1/2)*10*8 = 40 in²

Semicircle: diameter = 10 in → radius = 5 in
Area of full circle = πr² = 3.14 × 25 = 78.5 in²
Semicircle = 78.5 ÷ 2 = 39.25 in²

Total area = 40 + 39.25 = 79.25 in²

✔ Final Answer for #6: 79.25

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Now compiling all final answers:

Final Answer:
1) 145.12
2) 110.00
3) 48.00
4) 81.00
5) 80.00
6) 79.25