1. **Problem Statement:** You want to calculate the area of two chosen putting green designs from three options: The Teardrop, The Point, and The Half Circle. 2. **Design Choice #1: The Teardrop** - The teardrop consists of a quarter circle plus a square inside it. - The square is 8 ft by 8 ft. - The quarter circle radius is 8 ft (since the square fits inside the quarter circle). 3. **Formula for area of a quarter circle:** $$\text{Area} = \frac{1}{4} \pi r^2$$ - Here, $r = 8$ ft. 4. **Calculate quarter circle area:** $$\frac{1}{4} \times 3.14 \times 8^2 = \frac{1}{4} \times 3.14 \times 64 = 50.24 \text{ ft}^2$$ 5. **Calculate square area:** $$8 \times 8 = 64 \text{ ft}^2$$ 6. **Total area of the teardrop:** $$50.24 + 64 = 114.24 \text{ ft}^2$$ --- 7. **Design Choice #2: The Point** - The shape is a polygon made of a rectangle and a triangle on top. - Rectangle base = 12 ft, height = 6 ft. - Triangle base = 6 ft, height = 4 ft (since total height is 10 ft and rectangle is 6 ft tall). 8. **Calculate rectangle area:** $$12 \times 6 = 72 \text{ ft}^2$$ 9. **Calculate triangle area:** $$\frac{1}{2} \times 6 \times 4 = 12 \text{ ft}^2$$ 10. **Total area of the point:** $$72 + 12 = 84 \text{ ft}^2$$ --- 11. **Choosing between the two designs:** - The Teardrop has an area of $114.24$ ft$^2$. - The Point has an area of $84$ ft$^2$. - If you want more turf area, choose the Teardrop. --- 12. **Cost estimation:** - Cost per square foot = 5.85 - For Teardrop: $$114.24 \times 5.85 = 668.9$$ - For Point: $$84 \times 5.85 = 491.4$$ **Final answers:** - Area of Teardrop: $114.2$ ft$^2$ (rounded to nearest tenth) - Area of Point: $84.0$ ft$^2$ - Estimated cost for Teardrop turf: 669 - Estimated cost for Point turf: 491