Answer:
\(A_{shaded}= 136.96 ft^{2}\)
Step-by-step explanation:
We will find the shaded area if we subtract the area of the triangle from the area of the circle.
We know that the area of the circle is defined as
\(A= \pi r^{2}\)
Where \(r\) is half the diameter, that is
\(r=\frac{16ft}{2}=8ft\)
The area of the circle is
\(A= \pi r^{2}\\A= 3.14 (8ft)^{2} =200.96ft^{2}\)
Now, we have to find the area of the triangle, which is defined as
\(A_{\triangle} =\frac{bh}{2}\)
Where \(b\) is the base of 16 feet, and \(h\) is the height of the triangle which is on the radius. So, we have \(b=16ft\) and \(h=8ft\).
The area of the triangle is
\(A_{\triangle} =\frac{16ft(8ft)}{2}=64ft^{2}\)
Now, the shaded is the difference as we said before, that is
\(A_{shaded}=A-A_{\triangle}\)
Replacing both areas, we have
\(A_{shaded}=200.96 ft^{2} - 64ft^{2}= 136.96 ft^{2}\)
Therefore, the shaded area is \(A_{shaded}= 136.96 ft^{2}\)
