Question

If the perimeter of a rhombus is $4a$ and the lengths of the diagonals are $x$ and $y$, then its area is

• A. $a(x+y)$
• B. $x^2+y^2$
• C. $xy$
• D. $\frac{xy}{2}$

Answer 1

The correct option is D

$\frac{xy}{2}$

Calculate the area of rhombus

Given: Perimeter of a rhombus = $4a$

and the lengths of the diagonals are $x$ and $y$

We know that, Area of rhombus = $\frac{1}{2}\times$ product of diagonals

$$\begin{gathered} =\frac{1}{2}\times \left(x\right)\times \left(y\right) \\ =\frac{xy}{2} \end{gathered}$$

So , the area of the rhombus is $\frac{xy}{2}$.

Hence, if the perimeter of a rhombus is $4a$ and the lengths of the diagonals are $x$ and $y$, then its area is $\frac{xy}{2}$.

Hence, option (D) is the correct answer.