Question

In the following figure, O is the centre of a circular arc and AOB is a straight line. Find the perimeter and the area of the shaded region correct to one decimal place. (Take π = 3.142)

Answer 1

(i) Let us find the perimeter of the shaded region.

Therefore, perimeter of the shaded region is .

Now we will find the area of the shaded region can be calculated as shown below,

Area of the shaded region = Area of the semi-circle − area of the right angled triangle

First, we will find the length of AB as shown below,

Substituting we get,

Therefore, area of the shaded region is.