Let H be the intersection point of AB and O1O2.
- First compute the measure (in radians) of
Consider the triangle , which is a right angle triangle.
We know that
- Now compute the area of the arc of circle
I'm too rusty to remember if there is a formula for it, but here is the reasoning.
The whole circle has a center angle of radians.
The arc of circle we consider has a center angle of radians.
So basically, we're considering th of the circle.
It can be used for the area :
- You now have to substract the area of the triangle to get half of the shaded area.
Note that has twice the area of
So let's consider the triangle .
It's a right angle triangle.
By the Pythagorean theorem,
So the area of this triangle is
Twice this area = area of triangle = 48 cm².
So the area of half the shaded area is
Hence the shaded area is
I hope it's clear enough