1. **Stating the problem:** We have a composite figure consisting of a rectangle with a slanted left side and a semicircle attached at the base. The rectangle's top width is 9 ft, the slanted left side drops down 7 ft, and the full height on the right side is 26 ft. We want to analyze or find properties such as area or perimeter of this figure. 2. **Understanding the shape:** The figure can be divided into two parts: - A trapezoid formed by the top rectangle and the slanted left side. - A semicircle attached to the base of the trapezoid. 3. **Formulas used:** - Area of trapezoid: $$A_{trap} = \frac{1}{2} (b_1 + b_2) h$$ where $b_1$ and $b_2$ are the two parallel sides and $h$ is the height. - Area of semicircle: $$A_{semi} = \frac{1}{2} \pi r^2$$ where $r$ is the radius. 4. **Identify dimensions:** - Top base $b_1 = 9$ ft. - Height of trapezoid $h = 26$ ft (right side height). - The slanted left side drops 7 ft, so the bottom base $b_2 = 9 + 7 = 16$ ft (assuming horizontal projection). - The semicircle is attached at the base, so its diameter equals the bottom base $b_2 = 16$ ft, thus radius $r = \frac{16}{2} = 8$ ft. 5. **Calculate trapezoid area:** $$A_{trap} = \frac{1}{2} (9 + 16) \times 26 = \frac{1}{2} \times 25 \times 26 = 12.5 \times 26 = 325 \text{ ft}^2$$ 6. **Calculate semicircle area:** $$A_{semi} = \frac{1}{2} \pi (8)^2 = \frac{1}{2} \pi \times 64 = 32\pi \approx 100.53 \text{ ft}^2$$ 7. **Total area of composite figure:** $$A_{total} = A_{trap} + A_{semi} = 325 + 32\pi \approx 325 + 100.53 = 425.53 \text{ ft}^2$$ **Final answer:** The total area of the composite figure is approximately **425.53 ft²**.