Question

The perimeter of the rhombus is $52$ cm. If one of the diagonal is $24$ cm, then find the area of the rhombus in $c{m}^2$.

Answer 1

Side of a rhombus=$\frac{1}{4}\times 52cm$
=13cm
Let AC = 24cm so that
$AO=\frac{1}{2}\times 24cm$
=12cm
$\therefore O{B}^2=A{B}^2-O{A}^2$
=(169-144)=25
or OB=5 and thus BD=2.OB=$2\times 5=10cm$
Area of the rhombus $=\frac{1}{2}\times 24\times 10$
$=120c{m}^2$