Question

If the diagonals of a rhombus get doubled, then the area of the rhombus becomes __________ its original area.

Answer 1

Compute the required value.

A rhombus is a special case of a parallelogram, and it is a four-sided quadrilateral having all equal sides. In a rhombus, opposite sides are parallel and the opposite angles are equal.

Let $p$ and $q$ be the two diagonals of the rhombus.

We know that area of the rhombus is given by:

$A=\frac{pq}{2}$

Given: Diagonals of the rhombus get doubled.

Therefore,

$$\begin{gathered} A\text{'}=\frac{\left(2p\right)\left(2q\right)}{2} \\ \Rightarrow A\text{'}=\frac{4pq}{2} \\ \Rightarrow A\text{'}=4A \end{gathered}$$

Hence, If the diagonals of a rhombus get doubled, then the area of the rhombus becomes $4$ times of its original area.