Question

Question 32

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

Answer 1

4 times
We know that,
Area of a rhombus $=\frac{1}{2}\times d_1\times d_2$
where, $d_1$ and $d_2$ are diagonals of the rhombus.
If diagonals get doubled, then the new diagonals are $2d_1$ and $2d_2$
Therefore, Area $=\frac{1}{2}2d_1\times 2d_2=4(\frac{1}{2}\times d_1\times d_2)$
Hence, the new area becomes 4 times its original area.