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
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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