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

Answer: Option C

Solution

Answer: Option C

Solution:

$$\begin{array}{rl}& \text{Using Hero’s formula}\\ & \text{S}=\frac{15+7+20}{2}=21\text{ cm}\\ & \text{Area of }\Delta \text{ABC}=\sqrt{21\left(21-20\right)\left(21-7\right)\left(21-15\right)}\\ & =\sqrt{21\times 1\times 14\times 6}\\ & =42\text{ c}{\text{m}}^2\\ & \Rightarrow \text{Area of }\square \text{ABCD}=42\times 2=84\text{ c}{\text{m}}^2\end{array}$$