1. **State the problem:** Find the area of a composite figure consisting of a rectangle and a semicircle on the top-right. 2. **Identify dimensions:** The rectangle has height $11$ yd and base $7$ yd (bottom horizontal). The semicircle is attached on the top-right side with a diameter equal to the top-right horizontal segment $2$ yd. 3. **Formula for area of rectangle:** $$\text{Area}_{\text{rectangle}} = \text{base} \times \text{height}$$ 4. **Formula for area of semicircle:** $$\text{Area}_{\text{semicircle}} = \frac{1}{2} \pi r^2$$ where $r$ is the radius of the semicircle. 5. **Calculate rectangle area:** $$\text{Area}_{\text{rectangle}} = 7 \times 11 = 77$$ 6. **Calculate radius of semicircle:** $$r = \frac{2}{2} = 1$$ 7. **Calculate semicircle area:** $$\text{Area}_{\text{semicircle}} = \frac{1}{2} \pi (1)^2 = \frac{\pi}{2} \approx 1.5708$$ 8. **Calculate total area:** $$\text{Area}_{\text{total}} = 77 + 1.5708 = 78.5708$$ 9. **Round to nearest hundredth:** $$78.57$$ **Final answer:** The area of the figure is approximately **78.57** square yards.