Question

Find the area of one segment formed by a square with sides of 6" inscribed in a circle.

(Hint: use the ratio of 1:1:√2 to find the radius of the circle.)

Answer 1

the answer is 9/2 pi - 9
but how?

Answer 2

diameter of the circle is the diagonal of the square. since the square has side 6, we know the diameter of the circle is
\[d=6\sqrt{2}\]
and so the radius is
\[3\sqrt{2}\]
area of square is 36
area of circle is
\[\pi r^2=\pi (3\sqrt{2})^2=18\pi\]

Answer 3

so we know the area of the square, and we know the area of the circle. if we knew what 'ONE SEGMENT' meant i we would be done

Answer 4

\[\frac{18(\pi-2)}{4}=\frac{9(\pi-2)}{2}\]