1. **Problem 1: Find the blue area on the basketball court.** The blue area is a rectangle with dimensions 12 ft by 19 ft. Formula for area of rectangle: $$\text{Area} = \text{length} \times \text{width}$$ Calculate: $$\text{Area}_{blue} = 12 \times 19 = 228 \text{ square feet}$$ 2. **Problem 2: Find the red area on the basketball court.** The red area is a semicircle with radius 6 ft. Formula for area of a circle: $$\pi r^2$$ Area of semicircle: $$\frac{1}{2} \pi r^2$$ Calculate: $$\text{Area}_{red} = \frac{1}{2} \pi (6)^2 = \frac{1}{2} \pi 36 = 18\pi \approx 56.5 \text{ square feet}$$ Rounded to nearest foot: 57 square feet. 3. **Problem 3: Find the area to be carpeted in the family room.** The carpet area is a polygon. We split it into two rectangles: - Rectangle 1: 24 ft by 6 ft - Rectangle 2: 17 ft by 9 ft Calculate each area: $$\text{Area}_1 = 24 \times 6 = 144$$ $$\text{Area}_2 = 17 \times 9 = 153$$ Total carpet area: $$144 + 153 = 297 \text{ square feet}$$ 4. **Problem 4: Calculate the carpet cost.** Carpet cost is $4.86 per square yard. Convert square feet to square yards: $$1 \text{ square yard} = 9 \text{ square feet}$$ Calculate area in square yards: $$\frac{297}{9} = 33 \text{ square yards}$$ Calculate cost: $$33 \times 4.86 = 160.38$$ **Final answers:** - Blue area: 228 square feet - Red area: 57 square feet - Carpet area: 297 square feet - Carpet cost: 160.38