1. **State the problem:** We have a figure composed of a rectangle and a semicircle on top. The rectangle is 36 ft wide and 31 ft tall. The semicircle has its diameter equal to the top side of the rectangle (36 ft). We need to find: - The perimeter of the figure. - The area of the figure. 2. **Formulas and important rules:** - Perimeter of the figure = perimeter of rectangle without the top side + circumference of semicircle. - Area of the figure = area of rectangle + area of semicircle. Formulas: - Rectangle perimeter (all sides) = $2(\text{width} + \text{height})$ - Circumference of full circle = $2\pi r$ - Circumference of semicircle = $\pi r$ - Area of rectangle = $\text{width} \times \text{height}$ - Area of circle = $\pi r^2$ - Area of semicircle = $\frac{1}{2} \pi r^2$ 3. **Calculate radius of semicircle:** Diameter $d = 36$ ft, so radius $r = \frac{d}{2} = \frac{36}{2} = 18$ ft. 4. **Calculate perimeter:** The perimeter includes: - Two vertical sides of rectangle: $2 \times 31 = 62$ ft - Bottom side of rectangle: $36$ ft - Semicircle circumference: $\pi \times 18 = 18\pi$ ft So, $$\text{Perimeter} = 62 + 36 + 18\pi = 98 + 18\pi$$ Approximate $\pi \approx 3.1416$: $$18 \times 3.1416 = 56.5488$$ Therefore, $$\text{Perimeter} \approx 98 + 56.5488 = 154.55 \text{ ft}$$ 5. **Calculate area:** - Area of rectangle: $$36 \times 31 = 1116 \text{ ft}^2$$ - Area of semicircle: $$\frac{1}{2} \pi r^2 = \frac{1}{2} \pi (18)^2 = \frac{1}{2} \pi 324 = 162\pi$$ Approximate: $$162 \times 3.1416 = 508.94 \text{ ft}^2$$ - Total area: $$1116 + 508.94 = 1624.94 \text{ ft}^2$$ **Final answers:** - Perimeter $\approx 154.55$ ft - Area $\approx 1624.94$ ft$^2$