Réponse :
bonjour,
1-
AD = (x + 3)+(x-2) = x + 3 + x - 2 = 2x + 1
Aire ABCD = (2x + 1)²
Aire ABEF = (2x + 1 )×( x + 3 )
Aire ECDF = (2x + 1 )×( x - 2 ) = 2x² - 4x + x - 2 = 2x² - 3x - 2
2-
Aire ABEF ( B ) = (2x + 1 )×( x + 3 ) = 2x² + 6x + x + 3 = 2x² + 7x + 3
Aire ECDF ( C ) = (2x + 1 )×( x - 2 ) = 2x² - 4x + x - 2 = 2x² - 3x - 2
(2x² + 7x + 3 ) + ( 2x² - 3x - 2 )
= 2x² + 7x + 3 + 2x² - 3x - 2
Aire ABEF + Aire ECDF = 4x² + 4x + 1
Aire ABCD = (2x + 1)²
d'apres l'identité remarquable (a+b)² = a² + 2ab + b²
= (2x)² + 2×2x×1 + 1²
= 4x² + 4x + 1
Aire ABCD = Aire ABEF + Aire ECDF
voila :)
