From Gogeometry

Using :

• Additional points
• Thales theorem
• Area of a triangle

• Define S0=[ABCD], L midpoint of CD, I intersection of AB and CD and h the height of CBE and DAE
• [ECL]=EL*h/2 and [ELD]=EL*h/2 => [ECD]=EL*h
• [BCE]=BC*h/2 and [AED]=AD*h/2
• EL=(BC+AD)/2
• S0=[ECD]+[BCE]+[AED]=EL*h + (BC+AD)*h/2= EL*h + EL*h
• => [ECD]=[BCE]+[AED]=S0/2
• [AIG]=[GID] and [BIF]=[FIC] => [ABFG]=[DCFG]
• S0=[ABFG]+[DCFG] => [DCFG]=S0/2
• S0/2=[DCFG]= [ECD] =>S1+[CHMD]+S2= [CHMD]+S
• Therefore S=S1+S2