1. **Problem statement:** Find the area of a semicircle and a quarter circle each with radius $r=13$ miles. 2. **Formulas:** - Area of a full circle: $$A=\pi r^2$$ - Area of a semicircle (half circle): $$A_{semi}=\frac{1}{2}\pi r^2$$ - Area of a quarter circle: $$A_{quarter}=\frac{1}{4}\pi r^2$$ 3. **Calculate the area of the semicircle:** $$A_{semi}=\frac{1}{2}\pi (13)^2=\frac{1}{2}\pi 169=\frac{169}{2}\pi$$ 4. **Calculate the area of the quarter circle:** $$A_{quarter}=\frac{1}{4}\pi (13)^2=\frac{1}{4}\pi 169=\frac{169}{4}\pi$$ 5. **Simplify and approximate:** - Semicircle area: $$\frac{169}{2}\pi=84.5\pi\approx 265.36\text{ square miles}$$ - Quarter circle area: $$\frac{169}{4}\pi=42.25\pi\approx 132.68\text{ square miles}$$ **Final answers:** - Semicircle area: approximately 265.36 square miles - Quarter circle area: approximately 132.68 square miles