Math Qn

Someone posted the following question on the cbox:
Let AG be x cm.
Then GB = 12-x
Triangle AGF is similar to Triangle ABC, hence AG = GF = x
Tiangle BGF is similar to Triangle BAE, hence
BG/GF = BA/AE
=> (12-x)/x = 12/6 (since AB = 12, AE = 6)
=> 12-x = 2x
=> x=4
Area of Triangle DEF = 1/2 x ED x AG = 1/2 x 6 x 4 = 12
Area of Triangle DFC = 1/2 x DC x (BC - GF) = 1/2 x 12 x (12-4) = 48
Hence, Area of shaded region = 12 + 48 = 60 cm2.