# 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.

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

A1 = A1 = = m2

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

A2 = A2 = = m2

Therefore area of quadrilateral ABCD = A1 + A2 = 336+210 = 546 cm2

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