Solution:
To find the area of a composite shape, we need to break the composite shape into smaller "known" shapes.
- ⇒ Area of composite figure = Area of quarter circle + Area of all rectangles...
Step-1: Find the radius of the quarter circle
- Radius of quarter circle = (8 + 4 + 4) - (9)
- Radius of quarter circle = (16) - (9)
- Radius of quarter circle = 7 meters
Step-2: Find the area of the quarter circle (Q)
- Area of circle = πr²
- Area of quarter-circle = πr²/4
- Area of quarter-circle = (3.14)(7²)/4
- Area of quarter-circle = (0.785)(49)
- Area of quarter-circle = 38.465 m²
Step-3: Find the area of rectangle₁ (L)
- Area of rectangle = LB
- Area of rectangle₁ = (21)(8)
- Area of rectangle₁ = 168 m²
Step-4: Find the area of rectangle₂ (M)
- Area of rectangle = LB
- Area of rectangle₂ = (4 + 4)(21 - 18)
- Area of rectangle₂ = (8)(3)
- Area of rectangle₂ = 24 m²
Step-5: Find the area of rectangle₃ (S)
- Area of rectangle = LB
- Area of rectangle₃ = (4)(8)
- Area of rectangle₃ = 32 m²
Step-6: Find the area of the composite figure.
- Area of composite figure = Area of quarter circle + Area of all rectangles...
- Area of composite figure = 38.465 + (168 + 24 + 32)
- Area of composite figure = 262.465 m²
