Question

You are given a circle of radius 12. What is the segment area of an arc that is 90 degrees?

Answer 1

The segment area
`= 113.09\ unit^2`

Explanation:

Area of the segment =
`((\theta))/(360) * \pi r^2`,where
`\theta` is the angle.

We can also say that
`90\ degrees` is covered with one segment and we have total
`4` segments (quadrants),so area of the circle divided by
`4` will give us the segement area of the arc.

So area
`(\pi r^2 )/(4) =(\pi(12)^2)/(4) = 113.09\ units^2`

So the area of the segment
`= 113.09 \ units^2`