Question

A triangle is inside a circle where the triangle's base is on the circle's diameter as shown.

Answer 1

Area of a circle=pi x r^2= 3.14 x 8^2(half of the radius)=3.14 x 64=200.96

area of triangle= 1/2 bh=1/2(16)(8)=1/2(128)=64

200.96-64=136.96 sq.ft

Answer 2

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 $A_{shaded}= 136.96 ft^{2}$