1. **State the problem:** Find the area of a compound figure composed of a tall rectangle with a semicircle on the top-right and a rectangular notch on the right side. 2. **Identify the parts and dimensions:** - Left vertical side: 17 yd - Bottom horizontal side: 6 yd - Right vertical sides: 9 yd (lower) + 8 yd (upper) = 17 yd total - Top horizontal side: 5 yd (left) + semicircle diameter (6 yd) = 11 yd total - Rectangular notch: 3 yd wide (horizontal) and 8 yd tall (vertical) 3. **Calculate the area of the large rectangle before the notch and semicircle:** - Width = 6 yd (bottom side) - Height = 17 yd (left side) - Area = width \times height = $6 \times 17 = 102$ yd$^2$ 4. **Calculate the area of the rectangular notch:** - Width = 3 yd - Height = 8 yd - Area = $3 \times 8 = 24$ yd$^2$ 5. **Calculate the area of the semicircle on the top-right:** - Diameter = 6 yd (same as bottom width) - Radius $r = \frac{6}{2} = 3$ yd - Area of full circle = $\pi r^2 = \pi \times 3^2 = 9\pi$ - Area of semicircle = $\frac{9\pi}{2} = 4.5\pi \approx 14.14$ yd$^2$ 6. **Calculate the total area of the figure:** - Start with large rectangle area: 102 yd$^2$ - Subtract notch area: $102 - 24 = 78$ yd$^2$ - Add semicircle area: $78 + 14.14 = 92.14$ yd$^2$ 7. **Final answer:** $$\boxed{92.14 \text{ square yards}}$$