A parallelogram has sides 60 m and 40 m and one of its diagonals is 80 m long. Its area is

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& S\left(\Delta ABD\right)=\frac{60+80+40}{2}=90\\ & \text{ar }\Delta ABD=\sqrt{90\left(90-80\right)\left(90-60\right)\left(90-40\right)}\\ & =\sqrt{90\times 10\times 30\times 50}\\ & =300\sqrt{15}{\text{m}}^2\\ & \text{ar }\square ABCD=2\times \text{ar }\Delta ABD=600\sqrt{15}{\text{m}}^2\end{array}$$