Question

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

Answer 1

Let $A(3,0),B(4,5),C(-1,4),D(-2,-1)$

Diagnols are $AC,BD$

$AC=\sqrt{(3+1{)}^2+(0-4{)}^2}=4\sqrt{2}$

$BD=\sqrt{(4+2{)}^2+(5+1{)}^2}=6\sqrt{2}$

Area of triangle is $\frac{1}{2}\left(AC\right)\left(BD\right)=24$