Question

Find the area of a rhombus if its vertices are $A(3,0),B(4,5),C(-1,4)$ and $D(-2,-1)$ order.

Answer 1

rhombus : $(3,0),(4,5),(-1,4),(-2,-1)$

area $=\frac{1}{2}\times \left(AC\right)\times \left(BD\right)$

$=\frac{1}{2}\times \left(\sqrt{{(3+1)}^2+{\left(4\right)}^2}\right)\times \left(\sqrt{{(4+2)}^2+{\left(6\right)}^2}\right)=\frac{1}{2}\sqrt{32}\times \sqrt{72}$

$=\frac{1}{2}\times 4\sqrt{2}\times 6\sqrt{2}$

area of rhombus $=24$ sq units