1. **Problem statement:** Find the perimeter and area of a composite figure consisting of a rectangle, a quarter circle on the left, and a semicircle on the right. 2. **Given dimensions:** - Rectangle length $= 10$ m - Rectangle height $= 2$ m - Quarter circle radius $= 2$ m (same as rectangle height) - Semicircle diameter $= 2$ m, so radius $= 1$ m 3. **Formulas:** - Area of rectangle: $A_{rect} = \text{length} \times \text{height}$ - Area of quarter circle: $A_{q} = \frac{1}{4} \pi r^2$ - Area of semicircle: $A_{semi} = \frac{1}{2} \pi r^2$ - Perimeter includes the outer edges: rectangle top and bottom, quarter circle arc, semicircle arc, and the vertical side of the rectangle not covered by quarter circle. 4. **Calculate areas:** $$A_{rect} = 10 \times 2 = 20$$ $$A_{q} = \frac{1}{4} \pi (2)^2 = \frac{1}{4} \pi \times 4 = \pi$$ $$A_{semi} = \frac{1}{2} \pi (1)^2 = \frac{1}{2} \pi = 0.5\pi$$ 5. **Total area:** $$A_{total} = A_{rect} + A_{q} + A_{semi} = 20 + \pi + 0.5\pi = 20 + 1.5\pi$$ 6. **Calculate perimeter:** - Quarter circle arc length: $L_{q} = \frac{1}{4} \times 2\pi r = \frac{1}{4} \times 2\pi \times 2 = \pi$ - Semicircle arc length: $L_{semi} = \pi r = \pi \times 1 = \pi$ - Rectangle top length: $10$ - Rectangle bottom length: $10$ - Rectangle vertical side on right: $2$ (height) 7. **Sum perimeter parts:** $$P = L_{q} + L_{semi} + 10 + 10 + 2 = \pi + \pi + 10 + 10 + 2 = 2\pi + 22$$ 8. **Final answers:** - Area: $$A_{total} = 20 + 1.5\pi \approx 20 + 4.712 = 24.712 \text{ m}^2$$ - Perimeter: $$P = 2\pi + 22 \approx 6.283 \times 2 + 22 = 6.283 + 6.283 + 22 = 28.566 \text{ m}$$