1. **Problem statement:** Calculate the total area of a window shaped as a rectangle with length 9 ft and height 6 ft, capped on each short side by a semicircle with radius 3 ft. 2. **Formula and explanation:** - Area of rectangle: $A_{rect} = \text{length} \times \text{height}$ - Area of a full circle: $A_{circle} = \pi r^2$ - Area of a semicircle: $A_{semi} = \frac{1}{2} \pi r^2$ 3. **Calculate rectangle area:** $$A_{rect} = 9 \times 6 = 54 \text{ ft}^2$$ 4. **Calculate semicircle area:** Radius $r = \frac{6}{2} = 3$ ft $$A_{semi} = \frac{1}{2} \pi (3)^2 = \frac{1}{2} \pi 9 = \frac{9\pi}{2}$$ 5. **Total semicircle area (two semicircles):** $$2 \times \frac{9\pi}{2} = 9\pi$$ 6. **Total window area:** $$A_{total} = A_{rect} + 9\pi = 54 + 9\pi \approx 54 + 28.27 = 82.27 \text{ ft}^2$$ **Final answer:** The total area of the window is approximately $82.27$ square feet.