Question

The length of two adjacent sides of a parallelogram are respectively $51cm$ and $37cm$. One of its diagonals is $20cm$. Find the area of the parallelogram.

Answer 1

Consider $AB=51cm$, $BC=37cm$ and $AC=20cm$.

In $\Delta ABC$,

$s=\frac{a+b+c}{2}$

$=\frac{51+37+20}{2}$

$=54$

The area of $\Delta ABC$ is,

$A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$

$=\sqrt{54\left(54-51\right)\left(54-37\right)\left(54-20\right)}$

$=\sqrt{54\left(3\right)\left(17\right)\left(34\right)}$

$=\sqrt{93636}$

$=306c{m}^2$

The area of parallelogram is the twice of $\Delta ABC$,

$A=2\times 306$

$A=612c{m}^2$