Question

A parallelogram has sides $6cm$ and $4cm$ and one of its diagonals is $8cm$ then its area is:-

Answer 1

Diagonals of a parallelogram divide the parallelogram into two parts of equal area.

So, we can say that,

Area of parallelogram $=2\times$ Area of $△ABC$

Now, we will use herons formula to calculate the area of $△ABC,$

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

$=\frac{6+4+8}{2}$

$=\frac{18}{2}$

$=9cm$

$ar\left(ABC\right)=\sqrt{9(9-6)(9-4)(9-8)}$

$=\sqrt{9\times 3\times 5\times 1}$

$=3\sqrt{15}c{m}^2$

So, area of parallelogram $=$ $2\times 3\sqrt{15}$

$=6\sqrt{15}c{m}^2$.