Practice 4-9: Area of Irregular Shapes worksheet featuring 13 geometric figures to calculate area, including composite shapes and a real-world application involving Nevada.

I'll solve each problem step by step, finding the area of irregular shapes using π = 3.14.

Problem 1: L-shaped figure
- Rectangle: 8 × 5 = 40
- Rectangle: 3 × 4 = 12
- Total: 40 + 12 = 52

Problem 2: House shape (rectangle + triangle)
- Rectangle: 12 × 6 = 72
- Triangle: (1/2) × 12 × 4 = 24
- Total: 72 + 24 = 96

Problem 3: T-shape
- Top rectangle: 10 × 3 = 30
- Bottom rectangle: 4 × 6 = 24
- Total: 30 + 24 = 54

Problem 4: Stepped shape
- Bottom rectangle: 12 × 4 = 48
- Middle rectangle: 8 × 3 = 24
- Top rectangle: 4 × 2 = 8
- Total: 48 + 24 + 8 = 80

Problem 5: Semicircle on rectangle
- Rectangle: 10 × 6 = 60
- Semicircle: (1/2) × π × r² = (1/2) × 3.14 × 3² = (1/2) × 3.14 × 9 = 14.13
- Total: 60 + 14.13 = 74.13

Problem 6: Archway shape
- Rectangle: 12 × 8 = 96
- Semicircle: (1/2) × π × r² = (1/2) × 3.14 × 4² = (1/2) × 3.14 × 16 = 25.12
- Total: 96 + 25.12 = 121.12

Problem 7: Chevron/V-shape
- Large rectangle: 10 × 8 = 80
- Subtract triangle: (1/2) × 10 × 4 = 20
- Total: 80 - 20 = 60

Problem 8: Semicircle with rectangle cutout
- Full circle: π × r² = 3.14 × 5² = 3.14 × 25 = 78.5
- Rectangle: 6 × 4 = 24
- Area: 78.5 - 24 = 54.5

Problem 9: Square with semicircles
- Square: 8 × 8 = 64
- Four semicircles = 2 full circles: 2 × π × r² = 2 × 3.14 × 2² = 2 × 3.14 × 4 = 25.12
- Total: 64 + 25.12 = 89.12

Problem 10: Semicircle on rectangle
- Rectangle: 8 × 6 = 48
- Semicircle: (1/2) × π × r² = (1/2) × 3.14 × 4² = (1/2) × 3.14 × 16 = 25.12
- Total: 48 + 25.12 = 73.12

Problem 11: Capsule shape (rectangle + 2 semicircles)
- Rectangle: 12 × 6 = 72
- Two semicircles = 1 full circle: π × r² = 3.14 × 3² = 3.14 × 9 = 28.26
- Total: 72 + 28.26 = 100.26

Problem 12: Pentagon shape
- Rectangle: 10 × 8 = 80
- Triangle: (1/2) × 10 × 4 = 20
- Total: 80 + 20 = 100

Problem 13: Nevada approximation
- Rectangle: 300 × 200 = 60,000
- Triangle: (1/2) × 300 × 150 = 22,500
- Total: 60,000 + 22,500 = 82,500 square miles

Final Answer:
1. 52
2. 96
3. 54
4. 80
5. 74.13
6. 121.12
7. 60
8. 54.5
9. 89.12
10. 73.12
11. 100.26
12. 100
13. 82,500 square miles