1. **State the problem:** We need to find the area of a compound figure composed of a large semicircle on top, a vertical rectangular stem, a right-side rectangular extension, and a left lower cut-in, with given side lengths. 2. **Identify the shapes and dimensions:** - Semicircle radius: Since the top is 7 km wide, radius $r = \frac{7}{2} = 3.5$ km. - Vertical rectangular stem: height 5 km, width 4 km. - Right-side rectangular extension: 4 km by 4 km. - Left lower cut-in: 3 km by 4 km. 3. **Calculate the area of the semicircle:** $$\text{Area}_{semicircle} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (3.5)^2 = \frac{1}{2} \pi \times 12.25 = 6.125\pi$$ 4. **Calculate the area of the vertical rectangular stem:** $$\text{Area}_{stem} = 5 \times 4 = 20$$ 5. **Calculate the area of the right-side rectangular extension:** $$\text{Area}_{right} = 4 \times 4 = 16$$ 6. **Calculate the area of the left lower cut-in:** $$\text{Area}_{left} = 3 \times 4 = 12$$ 7. **Calculate total area:** Add the semicircle, stem, and right extension, then subtract the left cut-in: $$\text{Total Area} = 6.125\pi + 20 + 16 - 12 = 6.125\pi + 24$$ 8. **Evaluate the numerical value:** Using $\pi \approx 3.1416$: $$6.125 \times 3.1416 = 19.24$$ $$\text{Total Area} = 19.24 + 24 = 43.24$$ 9. **Final answer:** The area of the figure is approximately **43.24 square kilometers**.