Math worksheet featuring nine problems where students must find the area of various compound shapes.

Let's solve each compound shape step by step. We'll break down each figure into simpler shapes (rectangles, triangles, semicircles), calculate their areas, and then sum them up.

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1)

Shape: Rectangle with a semicircle on top
- Rectangle: 16 cm × 8 cm = 128 cm²
- Semicircle: radius = 8 cm → area = (1/2)πr² = (1/2)π(8)² = (1/2)π(64) ≈ 100.53 cm²
- Total Area = 128 + 100.53 ≈ 229 cm²

> ✔ Answer: 229 cm²

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2)

Shape: Right triangle with a quarter circle attached
- Triangle: base = 27 cm, height = 9 cm → area = (1/2) × 27 × 9 = 121.5 cm²
- Quarter circle: radius = 9 cm → area = (1/4)πr² = (1/4)π(81) ≈ 63.62 cm²
- Total Area = 121.5 + 63.62 ≈ 185 cm²

> ✔ Answer: 185 cm²

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3)

Shape: Rectangle with a semicircle on top
- Rectangle: 24 m × 18 m = 432 m²
- Semicircle: radius = 7 m → area = (1/2)π(7)² = (1/2)π(49) ≈ 76.97 m²
- Total Area = 432 + 76.97 ≈ 509 m²

> ✔ Answer: 509 m²

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4)

Shape: L-shaped figure → can be split into two rectangles
- Left rectangle: 10 cm × 5 cm = 50 cm²
- Right rectangle: 5 cm × 5 cm = 25 cm²
- Total Area = 50 + 25 = 75 cm²

> ✔ Answer: 75 cm²

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5)

Shape: Rectangle with semicircles on both ends (like a stadium)
- Rectangle: 36 cm × 24 cm = 864 cm²
- Two semicircles = one full circle: radius = 12 cm → area = π(12)² = 452.39 cm²
- Total Area = 864 + 452.39 ≈ 1316 cm²

> ✔ Answer: 1316 cm²

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6)

Shape: T-shaped figure → split into three rectangles
- Top rectangle: 18 cm × 18 cm = 324 cm²
- Middle rectangle: 30 cm × 18 cm = 540 cm²
- But wait — better to split vertically:
- Top: 18×18 = 324
- Bottom: 30×18 = 540
- But overlapping? No — actually, it's like a "T" with a horizontal bar on top of a vertical bar.

Wait: Let's re-analyze:

It’s a T-shape:
- Top rectangle: 18 cm wide × 18 cm high = 324 cm²
- Vertical rectangle below: 18 cm wide × 18 cm high = 324 cm²
- But the bottom part is 30 cm wide → so actually:

Better: Split into:
- Top: 18 cm × 18 cm = 324 cm²
- Bottom: 30 cm × 18 cm = 540 cm²
But the top is centered over the bottom → no overlap in area.

So total = 324 + 540 = 864 cm²

Wait — but the bottom is 30 cm wide and 18 cm tall, and the top is 18 cm wide and 18 cm tall — they are stacked.

So yes, total area = 324 + 540 = 864 cm²

> ✔ Answer: 864 cm²

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7)

Shape: House-like shape — triangle on top of a rectangle
- Triangle: base = 14 m, height = 21 m → area = (1/2)(14)(21) = 147 m²
- Rectangle: 14 m × 6 m = 84 m²
- Total Area = 147 + 84 = 231 m²

> ✔ Answer: 231 m²

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8)

Shape: Step-like shape — can be split into three rectangles or two rectangles

Break into:
- Top rectangle: 8 m × 8 m = 64 m²
- Bottom rectangle: 16 m × 4 m = 64 m²
- Total = 64 + 64 = 128 m²

> ✔ Answer: 128 m²

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9)

Shape: Right triangle with a semicircle on the base
- Triangle: base = 4 m, height = 9 m → area = (1/2)(4)(9) = 18 m²
- Semicircle: radius = 4 m → area = (1/2)π(4)² = (1/2)π(16) ≈ 25.13 m²
- Total Area = 18 + 25.13 ≈ 43 m²

> ✔ Answer: 43 m²

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✔ Final Answers:

1) 229 cm²
2) 185 cm²
3) 509 m²
4) 75 cm²
5) 1316 cm²
6) 864 cm²
7) 231 m²
8) 128 m²
9) 43 m²

All rounded to nearest whole number as requested.

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