Question

finn recently completed a landscaping project on his property and wants to plant grass seed for the area shown in the figure below. how many square feet will he need to plant with grass seed? use 3.14 or a calculator button for pi and provide an answer accurate to the nearest tenth.

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\). Here, the length of the rectangle is \(28\) ft and the width is \(10 + 13=23\) ft. So, \(A_{rectangle}=28\times23 = 644\) square - feet.

Step2: Calculate the area of the quarter - circle

The formula for the area of a full - circle is \(A=\pi r^{2}\). For a quarter - circle, \(A_{quarter - circle}=\frac{1}{4}\pi r^{2}\). The radius \(r = 10\) ft. Using \(\pi = 3.14\), we have \(A_{quarter - circle}=\frac{1}{4}\times3.14\times10^{2}=\frac{1}{4}\times3.14\times100 = 78.5\) square - feet.

Step3: Calculate the total area

The total area \(A = A_{rectangle}+A_{quarter - circle}\). Substituting the values we found: \(A=644 + 78.5=722.5\) square - feet.

Answer:

\(722.5\) square feet.