Question

If A (-3, 5), B (-2, -7), C (1, -8) and D (6, 3) are the vertices of a quadrilateral ABCD, find its area.

Answer 1

If the vertices of a quadrilateral are $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3)$ and $(x_4,y_4)$, its area is given by

$\frac{1}{2}|(x_1{y}_2-y_1{x}_2)+(x_2{y}_3-y_2{x}_3)+(x_3{y}_4-y_3{x}_4)+(x_4{y}_1-y_4{x}_1)|$

$=\frac{1}{2}|\left(\right(-3)\times (-7)-5\times (-2\left)\right)+\left(\right(-2)\times (-8)-(-7)\times 1)+(1\times 3-(-8)\times 6)+(6\times 5-3\times (-3\left)\right)|$

= 72 sq. units