Question

The perimeter of a rhombus is 52 cm. If one diagonal is 24 cm, then its area is ___ $c{m}^2$.

• A. 240
• B. 100
• C. 120
• D. 140

Answer 1

The correct option is C

120

Let the side of the rhombus be 'a'.

4a = 52

a = 13 cm

We know diagonals of a rhombus bisect each other at ${90}^{\circ }$

In $\Delta ABO$, $B{O}^2={13}^2-{12}^2$

$B{O}^2=5^2$

$BO=5cm$

$\therefore BD=10cm$

Area of rhombus $=\frac{1}{2}{d}_1{d}_2$

$=\frac{1}{2}\times 10\times 24$

$=120c{m}^2$

Hence (c)