Question

The diagonals of a rhombus are 18 cm and 24 cm. Find ;

(i) its area

(ii) length of its sides

(iii) its perimeter

Answer 1

Diagonal of rhombus are 18 cm and 24 cm.

$\therefore$ of rhombus =\frac{1}{2}\times\) Product of diagonals

$=\frac{1}{2}\times 18\times 24$

$=216c{m}^2$

(ii) $\because$ Diagonals of rhombus bisect each other at right angles.

$\therefore OA=\frac{1}{2}\times 24=12cm$

$OB=\frac{1}{2}\times 18=9cm$

In right $\angle d\Delta AOB$

$AB=\sqrt{O{A}^2+O{B}^2}$

$=\sqrt{(12{)}^2+(9{)}^2}$

$=\sqrt{144+81}$

$=\sqrt{225}=15cm$

$\therefore$ Side of rhombus =15 cm

(iii)Perimeter of rhombus $=4\times$ side

$=4\times 15=60cm$

(i)216 $c{m}^2$ (ii)15 cm (iii)60 cm