**Area of a Triangle:** We have already learned in practical geometry that the area of a trapezium is one half the sum of the lengths of two parallel sides multiplied by the perpendicular distance between them. Using this formula, we shall now derive an algebraic formula for the area of a triangle when the coordinates of the vertices are given

A = 1/2[x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})]