bonjour,
AC : AC est la diagonale du carré ABCD = a√2 ou avec pythagore
AC² = AB²+BC²
= a²+a²
= 2a²
AC = a√2
AO : demi-diagonale = a√2/2
SO : SOA rectangle en O
SO² = SA²-AO²
= a²-(a√2/2)²
= a²-2a²/4
= (4a²-2a²)/4
= 2a²/4
SO = a√2/2
V SABCD = 1/3(a²*a√2/2) = a^3√2/6
si a = √2
V = (√2)^3*√2/6 = 2√2*√2/6 = 4/6 = 1/3cm^3
