Worksheet for calculating the area of compound figures using geometric shapes.
A worksheet titled "Area of Compound Figures" with six geometric shapes made of rectangles and triangles, each labeled with dimensions for calculating area.
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Show Answer Key & Explanations
Step-by-step solution for: Area of Composite Shapes (Compound Figures) Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Area of Composite Shapes (Compound Figures) Worksheets
To find the area of the shaded region in each figure, we’ll break each shape into simpler parts (like rectangles, triangles, or semicircles), calculate their areas, and then add or subtract as needed. We’ll round all answers to two decimal places.
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Problem 1:
This is a rectangle with a semicircle on the right end.
- Rectangle: length = 15, width = 7 → Area = 15 × 7 = 105
- Semicircle: diameter = 7 → radius = 3.5 → Area = (π × 3.5²) / 2 ≈ (3.1416 × 12.25) / 2 ≈ 19.24
Total area = 105 + 19.24 = 124.24
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Problem 2:
This is a triangle attached to a semicircle.
- Triangle: base = 16, height = 12 → Area = (1/2) × 16 × 12 = 96
- Semicircle: diameter = 12 → radius = 6 → Area = (π × 6²) / 2 = (3.1416 × 36) / 2 ≈ 56.55
Total area = 96 + 56.55 = 152.55
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Problem 3:
This is a trapezoid? Actually, it’s a rectangle with a triangle on top.
Wait — looking again: it’s a rectangle (width 12, height 15) with a triangle on the left side? No — actually, it looks like a rectangle with a triangular extension on the left.
Actually, better to see it as:
- A rectangle: 12 wide × 15 tall → Area = 180
- A triangle on the left: base = 15 (same height), height = 7 (horizontal) → Area = (1/2) × 15 × 7 = 52.5
But wait — the triangle is attached to the left side, so total area = rectangle + triangle = 180 + 52.5 = 232.50
Alternatively, if you think of it as a trapezoid: parallel sides are 12 and (12+7)=19? No — that doesn’t fit.
Actually, the figure shows a rectangle 12×15, and a triangle sticking out to the left with base 15 and height 7 — yes, so adding them is correct.
Final: 232.50
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Problem 4:
This is an L-shaped figure. Break into two rectangles.
Option 1:
- Top rectangle: 8 wide × 5 tall → Area = 40
- Bottom rectangle: 4 wide × 10 tall → Area = 40
Total = 40 + 40 = 80.00
Option 2 (alternative split):
- Left rectangle: 4 wide × 15 tall → 60
- Right rectangle: 4 wide × 5 tall → 20
Total = 80 → same.
So, 80.00
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Problem 5:
L-shape again.
Break into:
- Top rectangle: 10 wide × 5 tall → 50
- Bottom rectangle: 5 wide × 10 tall → 50
Total = 50 + 50 = 100.00
Or:
- Left rectangle: 5 wide × 15 tall → 75
- Right rectangle: 5 wide × 5 tall → 25
Total = 100 → same.
Answer: 100.00
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Problem 6:
This is a pentagon — can be split into a rectangle and a triangle.
Rectangle: 10 wide × 18 tall → Area = 180
Triangle on bottom: base = 10, height = 5 → Area = (1/2) × 10 × 5 = 25
Total = 180 + 25 = 205.00
Wait — looking at the diagram: the triangle is pointing down, so yes, we add it.
Alternatively, if it were cut off, we’d subtract — but here it’s part of the shape, so add.
Final: 205.00
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Now, let’s double-check all calculations for accuracy.
1. 15×7=105; π×3.5²/2 = π×12.25/2 ≈ 38.4845/2? Wait — no:
π × 3.5² = 3.1416 × 12.25 = let’s compute:
3.1416 × 12 = 37.6992
3.1416 × 0.25 = 0.7854
Total = 38.4846
Divide by 2: 19.2423 → rounds to 19.24 → total 105 + 19.24 = 124.24 ✔
2. Triangle: 0.5×16×12=96
Semicircle: π×6²/2 = π×36/2 = 18π ≈ 56.5487 → 56.55 → total 152.55 ✔
3. Rectangle: 12×15=180
Triangle: 0.5×15×7=52.5 → total 232.50 ✔
4. Two rectangles: 8×5=40, 4×10=40 → 80 ✔
5. 10×5=50, 5×10=50 → 100 ✔
6. Rectangle: 10×18=180
Triangle: 0.5×10×5=25 → 205 ✔
All good.
Final Answer:
124.24, 152.55, 232.50, 80.00, 100.00, 205.00
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Problem 1:
This is a rectangle with a semicircle on the right end.
- Rectangle: length = 15, width = 7 → Area = 15 × 7 = 105
- Semicircle: diameter = 7 → radius = 3.5 → Area = (π × 3.5²) / 2 ≈ (3.1416 × 12.25) / 2 ≈ 19.24
Total area = 105 + 19.24 = 124.24
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Problem 2:
This is a triangle attached to a semicircle.
- Triangle: base = 16, height = 12 → Area = (1/2) × 16 × 12 = 96
- Semicircle: diameter = 12 → radius = 6 → Area = (π × 6²) / 2 = (3.1416 × 36) / 2 ≈ 56.55
Total area = 96 + 56.55 = 152.55
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Problem 3:
This is a trapezoid? Actually, it’s a rectangle with a triangle on top.
Wait — looking again: it’s a rectangle (width 12, height 15) with a triangle on the left side? No — actually, it looks like a rectangle with a triangular extension on the left.
Actually, better to see it as:
- A rectangle: 12 wide × 15 tall → Area = 180
- A triangle on the left: base = 15 (same height), height = 7 (horizontal) → Area = (1/2) × 15 × 7 = 52.5
But wait — the triangle is attached to the left side, so total area = rectangle + triangle = 180 + 52.5 = 232.50
Alternatively, if you think of it as a trapezoid: parallel sides are 12 and (12+7)=19? No — that doesn’t fit.
Actually, the figure shows a rectangle 12×15, and a triangle sticking out to the left with base 15 and height 7 — yes, so adding them is correct.
Final: 232.50
---
Problem 4:
This is an L-shaped figure. Break into two rectangles.
Option 1:
- Top rectangle: 8 wide × 5 tall → Area = 40
- Bottom rectangle: 4 wide × 10 tall → Area = 40
Total = 40 + 40 = 80.00
Option 2 (alternative split):
- Left rectangle: 4 wide × 15 tall → 60
- Right rectangle: 4 wide × 5 tall → 20
Total = 80 → same.
So, 80.00
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Problem 5:
L-shape again.
Break into:
- Top rectangle: 10 wide × 5 tall → 50
- Bottom rectangle: 5 wide × 10 tall → 50
Total = 50 + 50 = 100.00
Or:
- Left rectangle: 5 wide × 15 tall → 75
- Right rectangle: 5 wide × 5 tall → 25
Total = 100 → same.
Answer: 100.00
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Problem 6:
This is a pentagon — can be split into a rectangle and a triangle.
Rectangle: 10 wide × 18 tall → Area = 180
Triangle on bottom: base = 10, height = 5 → Area = (1/2) × 10 × 5 = 25
Total = 180 + 25 = 205.00
Wait — looking at the diagram: the triangle is pointing down, so yes, we add it.
Alternatively, if it were cut off, we’d subtract — but here it’s part of the shape, so add.
Final: 205.00
---
Now, let’s double-check all calculations for accuracy.
1. 15×7=105; π×3.5²/2 = π×12.25/2 ≈ 38.4845/2? Wait — no:
π × 3.5² = 3.1416 × 12.25 = let’s compute:
3.1416 × 12 = 37.6992
3.1416 × 0.25 = 0.7854
Total = 38.4846
Divide by 2: 19.2423 → rounds to 19.24 → total 105 + 19.24 = 124.24 ✔
2. Triangle: 0.5×16×12=96
Semicircle: π×6²/2 = π×36/2 = 18π ≈ 56.5487 → 56.55 → total 152.55 ✔
3. Rectangle: 12×15=180
Triangle: 0.5×15×7=52.5 → total 232.50 ✔
4. Two rectangles: 8×5=40, 4×10=40 → 80 ✔
5. 10×5=50, 5×10=50 → 100 ✔
6. Rectangle: 10×18=180
Triangle: 0.5×10×5=25 → 205 ✔
All good.
Final Answer:
124.24, 152.55, 232.50, 80.00, 100.00, 205.00
Parent Tip: Review the logic above to help your child master the concept of composite area worksheet pdf.
