Question

The sides of a quadrilateral, taken in order are 5, 12, 14 and 15 metres respectively, and the angle contained by the first two sides is a right angle. Find its area.

Answer 1

We assume ABCD be the quadrilateral having sides AB, BC, CD, DA and angle.

We take a diagonal AC, where AC divides quadrilateral ABCD into two triangles ΔABC and ΔADC. We will find the area of these two triangles and add them to find the area of the quadrilateral ABCD

In triangle ΔABC, we have

AB = 5 m; BC = 12 m

We will use Pythagoras theorem to calculate AC

AC² = AB² + BC²

Area of right angled triangle ΔABC, say A₁ is given by

Where, Base = AB = 5 m; Height = BC = 12 m

Area of triangle ΔADC, say A₂ having sides a, b, c and s as semi-perimeter is given by

Where, a = AC = 13 m; b = DC = 14 m; c = AD = 15 m

Area of quadrilateral ABCD, say A

A = Area of triangle ΔABC + Area of triangle ΔADC