Question

Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.

• A. 240 $c{m}^2$
• B. 480 $c{m}^2$
• C. 400 $c{m}^2$
• D. 550 $c{m}^2$

Answer 1

The correct option is A

240 $c{m}^2$

ABCD is a rhombus in which AB = BC = CD = DA = 17 cm
AC = 16 cm

Therefore, AO = 8 cm (Diagonals of a rhombus bisect each other at ${90}^{\circ }$.)
In ∆AOD,
$A{D}^2$ =$A{O}^2$ + $O{D}^2$
⇒ ${17}^2$ = $8^2$ +$O{D}^2$
⇒ 289 = 64 + $O{D}^2$
⇒ 225 = $O{D}^2$
⇒ OD = 15
Therefore, BD = 2 OD
= 2 $\times$ 15
= 30 cm
Hence, area of rhombus
= $\frac{1}{2}$ $\times$ 16 $\times$ 30
= 240 $c{m}^2$