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

Solution (By Examveda Team)

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