Question

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

Answer 1

$\left(i\right)$Area $=\left|\begin{array}{cc}0& 0\\ 4& 3\\ 6& 0\\ 0& 3\\ 0& 0\end{array}\right|=\frac{1}{2}|18+18|=18sq.units$

$\left(ii\right)$ Area $=\left|\begin{array}{cc}0& 0\\ a& 0\\ a& b\\ 0& b\\ 0& 0\end{array}\right|=\frac{1}{2}|ab+ab|=ab$