Question

CAB= DCA and and AD is parallel to BC, If area of BCD= 16 cm sq., find ar ABCD

Answer 1

Hii,,,
Angle CAB =angle DCA & AD||BC
Therefore, AC is the transversal of AD & BC.
As, AD||BC & AC is the transversal,
ABCD is a parallelogram.
A diagonal of a parallelogram divides it into 2 congruent triangle.
Therefore, BD bisects triangle ABD & triangle CDB into 2 condruent triangles.
i.e., triangle ABD=~triangle CBD
Therefore, ar (ABD) = ar (CBD) [Congruent triangles have equal areas]
But, ar (CBD)=16cm2
Therefore, ar (ABD)=16cm2
ar (ABCD)=ar (ABD)+ar (BCD)
=16 + 16 cm2
=32cm2
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