Bonjour,
1) aire ABCD = AD × DC = 10 × 6 = 60 cm²
2) aire CND = (CN × CD) ÷ 2 = (4 × 6) ÷ 2 = 12 cm²
3) a = AM donc aire AMD = 10a ÷ 2 = 5a cm²
4) AB = DC = 6 donc BM = AB - AM = 6 - a
5) aire BMN = (BN × BM) ÷ 2 = [(10 - 4) × (6 - a)] ÷ 2 = (6(6-a)) ÷ 2 = 3(6-a)
= 18 - 3a
6) aire MND = aire ABCD - (aire DNC + aire BMN + aire AMD)
= 60 - ( 12 + (18 - 3a) + 5a )
= 60 - (12 + 18 - 3a + 5a)
= 60 - 12 - 18 + 3a - 5a
= 30 - 2a
7) aire MND = 28
⇒ 30 - 2a = 28
⇒ 30 - 28 = 2a
⇒ 2 = 2a
⇒ a = 2/2
⇒ a = 1 cm
