Q. 93.8( 12 Votes )

# Find the area of a quadrilateral *ABCD* in which *AB* = 42 cm, *BC* = 21 cm, *CD* = 29 cm, *DA* = 34 cm and diagonal *BD* = 20 cm.

Answer :

In ∆ABD;

AB = a = 42 cm, BD = b = 20 cm, DA = c = 34 cm

Let a, b and c are the sides of triangle and s is

the semi-perimeter, then its area is given by:

A = where

= = 48

A_{1} =

A_{1} = = m^{2}

In ∆BCD;

BC = a = 21 cm, DC = b = 29 cm, BD = c = 20 cm

Let a, b and c are the sides of triangle and s is

the semi-perimeter, then its area is given by:

A = where

= = 35

A_{2} =

A_{2} = = m^{2}

Therefore area of quadrilateral ABCD = A_{1} + A_{2} = 336+210 = 546 cm^{2}

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