Question

The area of a rhombus, one side of which measures $25$ cm and diagonal $30$ cm, is

• A. $600c{m}^2$
• B. $250c{m}^2$
• C. $200c{m}^2$
• D. $150c{m}^2$

Answer 1

Answer: (A)

$600c{m}^2$

Given, Side $\left(x\right)=25$ cm; Diagonal, $d_1=30$ cm
If the other diagonal is $d_2$, then
$\Rightarrow 25=\frac{1}{2}\sqrt{d_1^2+d_2^2}$
$\Rightarrow 50=\sqrt{{30}^2+d_2^2}$
$\Rightarrow {50}^2={30}^2+d_2^2$
$\Rightarrow d_2^2={50}^2-{30}^2=80\times 20$
$\therefore d_2=40$ cm
Hence, area of rhombus $=\frac{1}{2}{d}_1\times d_2$
$\Rightarrow \frac{1}{2}\times 30\times 40$
$=600c{m}^2$