Let ABCD be a square with total area 1600. F is the midpoint of AD and E is the midpoint of FD. BE and CF intersect at G. Find the area of triangle EFG.
+128631 The sides = 40
FD = 20...so.....FE = 10
Note that triangle BGC is similar to triangle FGE
The base of triangle FGE = (1/4) of base of triangle FGE
So...the height of triangle FGE = must be (1/4) the height of triangle BGC
So height of BGC = 4 times height of FGE
So....
height of FGE + 4 *height of FGE = side length = 40
5 *height FGE = 40
height of FGE =40/5 = 8
So the area of triangle FGE =(1/2) FE * 8 = (1/2) (10)(8) = 40
