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.]
Re: Area triangle using determinant
)
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...
