• # question_answer A parallelogram has sides 15 cm and 7 cm long. The length of one of the diagonals is 20 cm. The area of the parallelogram is A)  42 $c{{m}^{2}}$                  B)  60 $c{{m}^{2}}$        C)  84 $c{{m}^{2}}$       D)  96 $c{{m}^{2}}$

(c): Area of parallelogram ABCD = Area of 2 $\Delta ABC$ Semi- perimeter of $\Delta ABC,S=\frac{20+7+15}{2}={{\frac{42}{2}}^{~}}=21cm$ $\therefore$area of $\Delta ABC=\sqrt{s\left( s-a \right)\left( s-b \right)\left( s-c \right)}$ $=\sqrt{21\left( 21-7 \right)\left( 21-20 \right)\left( 21-15 \right)}$ $=\sqrt{21\times 14\times 6}=42$sq.cm. $\therefore$Area of parallelogram $=2\times 42=84$sq. cm.