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 $AB=BC=CD=DA=17cm$
$AC=16cm$

Therefore, $AO=8cm$
In $△AOD$,
$A{D}^2=A{O}^2+O{D}^2$
$\Rightarrow {17}^2=8^2+O{D}^2$
$\Rightarrow 289=64+O{D}^2$
$\Rightarrow 225=O{D}^2$
$\Rightarrow OD=15$
Therefore, $BD=2OD$
$=2\times 15$
$=30cm$
Now, area of rhombus
$=\frac{1}{2}\times 16\times 30$
$=240c{m}^2$