Question

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

• A. $\frac{23}{2}squnit$
• B. $\frac{25}{2}squnit$
• C. $12$ sq unit
• D. none of these

Answer 1

The correct option is B $\frac{25}{2}squnit$

Let $A(1,2),B(4,-6)$ and $(3,5)$

Area of a triangle$=\Delta =\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]$

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

$=\frac{1}{2}[1(-11)+4\left(3\right)+3\left(8\right)]$

$=\frac{1}{2}[-11+12+24]=\frac{25}{2}$sq.units.