Question

If the vertices of a triangle are $(1,2),(4,-6)$ and $(3,5)$, then the area (in sq. units) of the triangle is

• A. $\frac{25}{2}$
• B. $12$
• C. $5$
• D. $25$

Answer 1

The correct option is A $\frac{25}{2}$

The area of the triangle is
$△=\frac{1}{2}\left|x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right|=\frac{1}{2}\left|1\right(-6-5)+4(5-2)+3(2+6\left)\right|=\frac{1}{2}|-11+12+24|=\frac{25}{2}\text{sq. units}$