Question

What is the area of the rhombus $ABCD$, if $AC=12cm$ and $BE=8cm$

• A. $384c{m}^2$
• B. $192c{m}^2$
• C. $48c{m}^2$
• D. $96c{m}^2$

Answer 1

The correct option is D

$96c{m}^2$

The diagonals of a rhombus bisect each other at right angles. Therefore, in the given figure:

$\Rightarrow BE=DE$

$\Rightarrow BD=BE+DE=2\times BE$

$\Rightarrow BD=2\times 8=16cm$

Now, area of the rhombus $=$ half of the product of the length of its diagonals.

$\Rightarrow \text{Area}=\frac{1}{2}\times AC\times BD$

$=\frac{1}{2}\times 12\times 16=96c{m}^2$