Question

Express answer in exact form. Show all work for full credit.Find the area of one segment formed by a 6" square inscribed in a circle.(Hint: use the ratio of 1:1: to find the radius of the circle.)

Answer 1

The area of the square is:

$\begin{gathered} As=6^2 \\ As=36in^2 \end{gathered}$

And the area of the circle is:

$\begin{gathered} Ac=\pi r^2 \\ Ac=\pi\cdot(3\sqrt[]{2})^2 \\ Ac=18\pi \end{gathered}$

The area of one segment is given by:

$\begin{gathered} A=\frac{Ac-As}{4} \\ A=\frac{18\pi-36}{4} \end{gathered}$