Question

Find the area of rhombus whose each side is equal to $15cm$ and one of its diagonal is $24cm$?

Answer 1

Let $ABCD$ is a rhombus with diagonals $AC$ and $BD$ which intersect each other at $O$.
$AC=24cm$
$\Rightarrow AO=12cm$
Let $BO=xcm$ and $AB=15cm$ (given)

By Pythagorean theorem,
$c^2=a^2+b^2$
$225=144+x^2$
$x^2=225–144$
$x^2=81$
$x=9cm$
$BO=9cm$
Diagonal $BD=2\times 9=18cm$
Area of Rhombus $=\frac{1}{2}\times \left[\text{Product of diagonals}\right]$
$=\frac{1}{2}\times 24\times 18$
Area $=216c{m}^2$
Therefore, area of the rhombus is $216c{m}^2$.