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Find the area if the shaded region in square inches.

Find the area if the shaded region in square inches.-example-1

1 Answer

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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.

User Andrey Kachow
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