Question

The length of one diagonal of the a rhombus of side $5cm$ is $8cm$. The area of rhombus is

• A. $40c{m}^2$
• B. $20c{m}^2$
• C. $26c{m}^2$
• D. $24c{m}^2$

Answer 1

The correct option is D $24c{m}^2$

The diagonals of the rhombus are perpendicular and bisect each other. $\therefore$, the diagonal of $8$ cm is divided into two segments $4$ cm long. Using the Pythagorean theorem and any of the right triangles to solve for $x$.

$5^2=4^2+x^2$

$\Rightarrow x^2=25-16=9$

$\therefore x=3$

Area of a rhombus$=\frac{1}{2}\times d_1\times d_2$

where $d_1=8cm$ and $d_2=3\times 2=6cm$

Area$=\frac{1}{2}\times 8\times 6=24$sq.cm

Hence area of the rhombus is $24sq.cm$