Bonjour,
Aire AMQ = (AM x AQ)/2 = (AM x (AD - DQ))/2 = (a x (5 - a)/2 = (5a - a²)/2
Aire CNP = Aire AMQ = (5a - a²)/2
Aire BMN = (BN x BM/2 = (BN x (AB - AM))/ = (a x (8 - a))/2 = (8a - a²)/2
Aire DPQ = Aire BMN = (8a - a²)/2
X = Aire ABCD - Aire AMQ - Aire CNP - Aire BMN - Aire DPQ
= Aire ABCD - 2 x Aire AMQ - 2 x Aire BMN
= 5 x 8 - (5a - a²) - (8a - a²)
= 40 - 5a + a² - 8a + a²
= 2a² - 13a + 40
Pour a = 1 : X = 2 - 13 + 40 = 29 cm²
Pour a = 5/2 : X = 2 x 5²/2² - 13x5/2 + 40 = 25/2 - 65/2 + 80/2 = 40/2 = 20 cm²
