Question

In the following figure, AB = 36 cm and M is mid-point of AB. Semi-circles are drawn on AB, AM and MB as diameters. A circle with centre C touches all the three circles. Find the area of the shaded region.

Answer 1

We have given two semi-circles and one circle.

Area of the shaded region = area of semicircle with diameter AB − area of two semicircles with diameters AM and MB - area of circle ……..(1)

Let us calculate the area of the semi-circle with AB as a diameter.

Now we will find the area of the semi-circle with AM as a diameter.

Area of the semi-circle with MB as a diameter is same as the area of the semi-circle with diameter with AM as a diameter.

Now we will find the area of the circle with centre C.

We know that radius of the circle is one sixth of AB.

Now we will substitute all these values in equation (1).

Therefore, area of shaded region is.