Hello,

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

Hence

So (radian)

- Now compute the area of the arc of circle

Note that

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,

That is

Hence

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