1. **State the problem:** We need to find the volume of an in-ground swimming pool with a water depth of 3.5 feet and then find the area of the solar cover for the pool. 2. **Analyze the pool shape:** The pool is a composite shape with dimensions: top side 32 ft, right side 24 ft, lower left section 22 ft, and left side 14 ft. 3. **Find the area of the pool surface (solar cover area):** - The pool outline is a polygon. We can divide it into simpler shapes or use the shoelace formula. 4. **Use the shoelace formula for polygon area:** Label vertices in order (clockwise or counterclockwise): Let the points be A(0,0), B(32,0), C(32,24), D(10,24), E(0,14) (assuming the shape based on given sides). 5. **Calculate area:** $$\text{Area} = \frac{1}{2} |x_1y_2 + x_2y_3 + x_3y_4 + x_4y_5 + x_5y_1 - (y_1x_2 + y_2x_3 + y_3x_4 + y_4x_5 + y_5x_1)|$$ Substitute: $$= \frac{1}{2} |0\times0 + 32\times24 + 32\times24 + 10\times14 + 0\times0 - (0\times32 + 0\times32 + 24\times10 + 24\times0 + 14\times0)|$$ $$= \frac{1}{2} |0 + 768 + 768 + 140 + 0 - (0 + 0 + 240 + 0 + 0)|$$ $$= \frac{1}{2} |1676 - 240| = \frac{1}{2} \times 1436 = 718 \text{ ft}^2$$ 6. **Find the volume:** Volume = Area \times Depth $$= 718 \times 3.5 = 2513 \text{ ft}^3$$ 7. **Final answers:** - Area of solar cover = 718 ft² - Volume of pool = 2513 ft³ These calculations assume the polygon vertices as described to match the given dimensions.