Question

Express answer in exact form.

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.)


help me please

Answer 1

We need to use the formula to find the area of a segment of a circle. \[A= (\theta/360)* \pi * r ^{2}\]
The square inside the circle will create four segments. So we know that is 1/4th of 360 degrees total. In other words, our angle is 90 degrees. We then just need to know the radius of the circle using the hint.

Answer 2

Let me correct that, the formula listed above is for the sector of a circle. Once we have the area of the sector, we subtract the area of one triangle and that will leave the segment.