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 \[c{{m}^{2}}\]

Correct Answer: C

Solution :

(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.