If the vertices of a triangle are $\left(1,2\right),\left(4,-6\right)and\left(3,5\right),$  then its area is

Area of the triangle whose vertices are given

$\Delta =\frac{1}{2}\left[x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right]$

$\Delta =\frac{1}{2}\left[1\left(-6-5\right)+4\left(5-2\right)+3\left(2+6\right)\right]$

$\Delta =\frac{25}{2}$  sq. units.