Thread: Area triangle using determinant

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.]

You could always expand this, re-arrange and see if you get a form that is equal to Area ADEC + Area CEFB - Area ADFB. In that case, you are done...