Question

in the village of hampton, the town committee is looking for estimates to mow the lawn at the town center. the area of grass to be mowed at the town center is 319.04 square feet, this excludes the area of a circular gazebo. the gazebo has a diameter of 16 feet. what is the area of the gazebo? what is the missing dimension of the town centers lawn? label your answers and show your work. substitute 3.14 for π. (7.g.6) (3 pts)

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\). Here, \(l = 20\) ft and \(w = 16\) ft.
\(A_{rectangle}=20\times16 = 320\) square feet.

Step2: Calculate the area of the circle

The formula for the area of a circle is \(A=\pi r^{2}\). Given the diameter \(d = 16\) ft, the radius \(r=\frac{d}{2}=\frac{16}{2}=8\) ft. Substitute \(\pi = 3.14\) and \(r = 8\) into the formula.
\(A_{circle}=3.14\times8^{2}=3.14\times64 = 200.96\) square feet.

Step3: Calculate the area of the lawn (area of the rectangle - area of the circle)

\(A = A_{rectangle}-A_{circle}\)
\(A=320 - 200.96=119.04\) square feet.

Answer:

The area of the gazebo (circle) is \(200.96\) square feet. The missing dimension (width of the rectangle) is \(16\) feet. The area of the lawn is \(119.04\) square feet.