Area of Composite Figures Worksheets - Math Monks - Free Printable

Let’s solve each problem step by step, using appropriate area formulas for regular polygons and composite figures.

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Problem 1: Rectangle

- Dimensions: width = 7.5 m, length = 10.9 m
- Area of rectangle = length × width
→ Area = 10.9 × 7.5 = 81.75 m²

✔ Answer: 81.75 m²

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Problem 2: Regular Pentagon

- Side length = 13.2 yd
- Apothem (distance from center to side) = 3.5 yd
- Formula for area of regular polygon:
Area = (1/2) × Perimeter × Apothem

Perimeter = 5 × side = 5 × 13.2 = 66 yd
→ Area = (1/2) × 66 × 3.5 = 33 × 3.5 = 115.5 yd²

✔ Answer: 115.5 yd²

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Problem 3: Regular Hexagon

- Side length = 12 cm
- Apothem = 5√3 cm

Regular hexagon has 6 sides → Perimeter = 6 × 12 = 72 cm
Area = (1/2) × Perimeter × Apothem
→ Area = (1/2) × 72 × 5√3 = 36 × 5√3 = 180√3 cm²

You can leave it in exact form or approximate:
√3 ≈ 1.732 → 180 × 1.732 ≈ 311.76 cm²
But since the apothem is given as exact (5√3), best to leave as 180√3 cm²

✔ Answer: 180√3 cm²

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Problem 4: Triangle

- Base = 22 in, Height = 16 in
- Area of triangle = (1/2) × base × height
→ Area = (1/2) × 22 × 16 = 11 × 16 = 176 in²

✔ Answer: 176 in²

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Problem 5: Composite Figure — Rectangle + Semicircle

- Rectangle: length = 32 ft, width = 18 ft
→ Area_rect = 32 × 18 = 576 ft²

- Semicircle: diameter = 18 ft → radius = 9 ft
→ Area_semicircle = (1/2) × π × r² = (1/2) × π × 81 = 40.5π ft²

Total Area = 576 + 40.5π ft²
Approximate: 40.5 × 3.1416 ≈ 127.23 → Total ≈ 576 + 127.23 = 703.23 ft²

But unless specified, leave in exact form:
✔ Answer: 576 + 40.5π ft² (or approximately 703.2 ft²)

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Problem 6: Composite Figure — Isosceles Triangle + Semicircle

- Triangle: base = 9 mm, height = total height - semicircle radius
Total height = 12 mm, semicircle diameter = 9 mm → radius = 4.5 mm
So triangle height = 12 - 4.5 = 7.5 mm

Area_triangle = (1/2) × 9 × 7.5 = 4.5 × 7.5 = 33.75 mm²

Area_semicircle = (1/2) × π × (4.5)² = (1/2) × π × 20.25 = 10.125π mm²

Total Area = 33.75 + 10.125π mm²
Approximate: 10.125 × 3.1416 ≈ 31.81 → Total ≈ 33.75 + 31.81 = 65.56 mm²

✔ Answer: 33.75 + 10.125π mm² (or approx 65.56 mm²)

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Problem 7: Composite Figure — Rectangle + Triangle

- Rectangle: length = 10 km, width = 6 km
→ Area_rect = 10 × 6 = 60 km²

- Triangle: base = 6 km (same as rectangle width), height = 4.8 km
→ Area_triangle = (1/2) × 6 × 4.8 = 3 × 4.8 = 14.4 km²

Total Area = 60 + 14.4 = 74.4 km²

✔ Answer: 74.4 km²

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Problem 8: Composite Figure — Square + Triangle

- Square: side = 16 cm
→ Area_square = 16 × 16 = 256 cm²

- Triangle: base = 16 cm (same as square side), height = 8.5 cm (given)
→ Area_triangle = (1/2) × 16 × 8.5 = 8 × 8.5 = 68 cm²

Total Area = 256 + 68 = 324 cm²

✔ Answer: 324 cm²

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## ✔ Final Answers:

1. 81.75 m²
2. 115.5 yd²
3. 180√3 cm²
4. 176 in²
5. 576 + 40.5π ft² (≈ 703.2 ft²)
6. 33.75 + 10.125π mm² (≈ 65.56 mm²)
7. 74.4 km²
8. 324 cm²

Let me know if you’d like diagrams or step-by-step visuals for any!