1. **State the problem:** Find the area of a figure composed of a rectangle and two semicircles attached to the shorter sides of the rectangle. 2. **Given dimensions:** Length of rectangle $=7$, height of rectangle $=6$. Each semicircle has diameter equal to the height of the rectangle, so diameter $d=6$. 3. **Formula for area:** - Area of rectangle: $A_{rect} = \text{length} \times \text{height} = 7 \times 6$ - Area of a circle: $A_{circle} = \pi r^2$ - Area of a semicircle: $A_{semi} = \frac{1}{2} \pi r^2$ 4. **Calculate radius of semicircle:** $$r = \frac{d}{2} = \frac{6}{2} = 3$$ 5. **Calculate area of rectangle:** $$A_{rect} = 7 \times 6 = 42$$ 6. **Calculate area of two semicircles (which together form a full circle):** $$A_{2semi} = 2 \times \frac{1}{2} \pi r^2 = \pi r^2 = \pi \times 3^2 = 9\pi$$ 7. **Calculate total area:** $$A_{total} = A_{rect} + A_{2semi} = 42 + 9\pi$$ 8. **Approximate numerical value:** $$9\pi \approx 9 \times 3.1416 = 28.2744$$ $$A_{total} \approx 42 + 28.2744 = 70.2744$$ 9. **Round to nearest tenth:** $$\boxed{70.3}$$ The area of the figure is approximately 70.3 square units.