Bonjour,
1) a) AD = AF + FD = (x+3) + (x-2) = x + x + 3 - 2 = 2x + 1
b) Aire ABCD = (AD)² = (2x+1)²
c) Aire ABEF = AF × AB = (x+3)(2x+1)
d) Aire ECDF = FD × CD = (x-2)(2x+1)
2)
a) Aire ABCD = (AD)² = (2x+1)² = 4x² + 4x + 1
Aire ABEF = AF × AB = (x+3)(2x+1) = 2x²+x+6x+3 = 2x²+7x+3
Aire ECDF = FD × CD = (x-2)(2x+1) = 2x²+x-4x-2 = 2x²-3x-2
b) Aire ABEF + Aire ECDF = (2x²+7x+3)+(2x²-3x-2)
= 2x²+2x²+7x-3x+3-2
= 4x²+4x+1
= Aire ABCD
