In this chapter, we will learn to calculate the area of quadrilateral when the length of all sides and measure of opposite angles are given.

After learning the formula, we will also try to solve some questions related to it.

Consider the below quadrilateral.

Here the length of sides are given as ” a “, ” b ” , ” c ” and ” d “.

Also measure of two opposite angles are given as ” 𝜃1 ” and ” 𝜃2 “

When in quadrilateral, the measure of all sides and opposite angles are given, you can apply following formula to get area of quadrilateral;

Area of Quadrilateral = \mathtt{\sqrt{( s-a)( s-b)( s-c)( s-d) -a.b.c.d.cos^{2}\frac{\theta }{2}}}

Where,

s = (a + b + c + d ) / 2

and, 𝜃 = 𝜃1 + 𝜃2

Please remember the above formula as its help solve related questions in the exams.