Question

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

Answer 1

Here, AB = 5 m, BC = 12 m, CD = 14 m and DA = 15 m 

Join the diagonal AC.

Now, area of △ABC = 1/2 x AB x BC 

= 1/2 x 5 x 12

= 30 

Area of △ABC is 30 m² 

In △ABC, (right triangle). 

From Pythagoras theorem, 

AC² = AB² + BC² 

AC² = 5² + 12² 

AC² = 25 + 144 = 169 

or AC = 13 

Now in △ADC, 

All sides are know, Apply Heron’s Formula:

Where a, b and c are sides of a triangle.

Perimeter of △ADC = 2s = AD + DC + AC 

2s = 15 m + 14 m + 13 m

s = 21 m

Area of △ADC = 84 m² 

Area of quadrilateral ABCD = Area of △ABC + Area of △ADC 

= (30 + 84) m² 

= 114 m²