Question

what is the area of this figure?
if necessary, round your answer to the nearest hundredth.
square yards

Explanation:

Step1: Calculate the area of the first rectangle

The first rectangle has length \(9\) yd and width \(2\) yd.
The area of a rectangle is \(A = l\times w\), so \(A_1=9\times2 = 18\) square yards.

Step2: Calculate the area of the second rectangle

The second rectangle has length \(7\) yd and width \(7\) yd.
Using the formula \(A = l\times w\), \(A_2 = 7\times7=49\) square yards.

Step3: Calculate the area of the third rectangle

The third rectangle has length \(9 - 2=7\) yd and width \(4\) yd.
Using the formula \(A = l\times w\), \(A_3=7\times4 = 28\) square yards.

Step4: Calculate the area of the semicircle

The diameter of the semicircle is \(9 - 2=7\) yd, so the radius \(r=\frac{7}{2}=3.5\) yd.
The area of a full - circle is \(A=\pi r^{2}\), and the area of a semicircle is \(A_{semicircle}=\frac{1}{2}\pi r^{2}\).
Substituting \(r = 3.5\) yd, \(A_{semicircle}=\frac{1}{2}\times\pi\times(3.5)^{2}=\frac{1}{2}\times\pi\times12.25\approx19.24\) square yards.

Step5: Sum up the areas

\(A=A_1 + A_2+A_3+A_{semicircle}\)
\(A=18 + 49+28+19.24\)
\(A=114.24\) square yards.

Answer:

\(114.24\)