Question

1. mary would like to plant grass in her backyard. her backyard is a rectangle that measures 10 yds by 8 yds. in the middle of her backyard is a circular swimming pool that has a diameter of 5 yds. what is the area to be planted with grass to the nearest tenth of a square yard?

a. 1.5 yd² c. 60.4 yd²
b. 19.6 yd² d. 80 yd²

Explanation:

Step1: Calculate area of rectangle

The formula for the area of a rectangle is \( A_{rectangle} = length \times width \). Given length = 10 yds and width = 8 yds, so \( A_{rectangle} = 10 \times 8 = 80 \) square yards.

Step2: Calculate area of circle

The formula for the area of a circle is \( A_{circle} = \pi r^2 \), where radius \( r = \frac{diameter}{2} \). The diameter is 5 yds, so \( r = \frac{5}{2} = 2.5 \) yds. Then \( A_{circle} = \pi \times (2.5)^2 \approx 3.1416 \times 6.25 \approx 19.635 \) square yards.

Step3: Calculate grass area

Subtract the area of the circle from the area of the rectangle: \( A_{grass} = A_{rectangle} - A_{circle} = 80 - 19.635 \approx 60.4 \) square yards.

Answer:

C. 60.4 yd²