Question

In the given figure, ABCD is a parallelogram. If area $\Delta ADP=30c{m}^2$ and area $\Delta BCP=24c{m}^2,$ then area of ||gm ABCD =___ $c{m}^2$

• A. 108
• B. 96
• C. 54
• D. 27

Answer 1

The correct option is A 108

(i)Through P draw PQ||AD||BC

(ii)APQD and PBCQ are parallelograms (opposits sides are parallel)

$\left(iii\right)\therefore$ area of ||gm APQD=$2\times area\Delta APD$

$=2\left(30\right)$ $=60c{m}^2$

(iv) area of ||gm PBCQ = $2\times area\Delta PBC$

=2(24) $=48c{m}^2$

$\therefore$ area ||gm ABCD = 60+48

$=108c{m}^2$