In the accompanying figure ,the area of the triangle can be expressed as

Area = Area + Area - Area

Use this and the fact that the area of trapezoid equal ½ of the altitude times the sum of the parallel sides to show that

[Note-in the derivation of this formula, the vertices are labelled such that the triangle is traced counter-clockwise proceeding from to to .for a clockwise orientation, the determinant above yields the negative of the area.]