Find the area if the shaded region in square inches.

Question

asked Jul 4, 2023 117k views

1 Answer

Andrey Kachow · Answer 1 · 2023-07-09T18:48:35+0000

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.

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