AC = AB√2 = 6√2 cm
A'C' = AC√2 = 4√2 cm
Ducem A'N ⊥ AC
AN = (6√2 - 4√2) : 2 = 2√2 : 2 = √2 cm
h = AN = OO' = √AA'² - AN² = √11 - 2 = √9 = 3 cm
Duc M'P ⊥ OM
MM'= √OO'² + (OM - O'M')²
= √9 + (3-2)²
= √9 + 1
= √10 cm
Al = (PB + Pb)·at/2 = (4·AB + 4·A'B')·MM'/2 = (4·6 + 4·4)·√10/2 = 20√10 cm²
VA = VA'+ A'A
VA'/VA = A'O'/AO
VA'/(VA'+A'A) = 2√2/3√2
3VA' = 2VA'+ 2√11
VA' = 2√11 cm
VO' = √4·11 - 2·2 = √40 = 2√10 cm
VO = 2√10 + 3 cm
V(VABCD) = Ab·H/3
= AB²· VO/3
= 36/3·(2√10 + 3)
= 12·(2√10 + 3) cm³
