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