Question

The diagonals of a rhombus $ABCD$ intersect at point $O$. Find the area of the rhombus, if $AO=4$ cm and $OD=5$ cm.

Answer 1

We know that in the rhombus the diagonals bisect perpendicularly.

Therefore, $AO=OC=4cm$ and $BO=OD=5cm$

$AC=AO+OC=4+4=8cm$

$BD=BO+OD=5+5=10cm$

Area of the rhombus $=\frac{AC\times BD}{2}=\frac{8\times 10}{2}=40c{m}^2$