In the diagram below, BE = EC = DF and ADF has the same area as DEF If rectangle DXYF has area 40, what is the area of DEF?

Note that triangles DXE and EYF have the same height as triangle DEF and their combined bases = DF

So.....their total areas must be the same as the area of triangle DEF

Since rectangle DXYF = 40......then it is composed of two equal areas .....

So.......[ DEF ] = 40 / 2 = 20