Question

Find the area if the shaded region in square inches.

Answer 1

First, we find the area of the circle.

`A=\pi r^2`

However, first, we have to find the diameter of the circle, which is the hypothenuse of the right triangle.

`\begin{gathered} h^2=21^2+20^2 \\ h=\sqrt[]{441+400} \\ h=\sqrt[]{841} \\ h=29 \end{gathered}`

So, the diameter is 29 inches long. Remember that the radius is half the diameter, 14.5 inches long. Let's find the area of the circle.

`A=\pi(14.5)^2=660.52in^2`

Now, we find the area of the triangle.

`A=(bh)/(2)=(20\cdot21)/(2)=210in^2`

At last, we subtract the area of the circle and the area of the triangle to find the shaded region.

`A_{\text{shaded}}=660.52-210=450.52in^2`

Hence, the answer is the first option.