Question

Find the area of the shaded region in the given figure.

Answer 1

We are given the following figure with dimensions.

Figure:

Let the point at which angle is be D.

AC = 52 cm, BC = 48 cm, AD = 12 cm, BD = 16 cm

We are asked to find out the area of the shaded region.

Area of the shaded region=Area of triangle ΔABC−area of triangle ΔABD

In right angled triangle ABD, we have

Area of the triangle ΔABD is given by

Whenever we are given the measurement of all sides of a triangle, we basically look for Heron’s formula to find out the area of the triangle.

If we denote area of the triangle by Area, then the area of a triangle having sides a, b, c and s as semi-perimeter is given by;

Where,

Here a = 48 cm, b = 52 cm, c = 20 cm and

Therefore the area of a triangle ΔABC is given by,

Now we have all the information to calculate area of shaded region, so

Area of shaded region = Area of ΔABC − Area of ΔABD

The area of the shaded region is 384 cm².