Răspuns:
a ) fie CD ⊥ AB
CD = AB√3/2 = 8√3×√3/2 = 4×3 = 12 cm (inaltimea bazei)
CO = 2CD/3 = 2×12/3 = 8 cm (raza cercului circumscris)
b) VD ⊥ AB
OD = CD - CO = 12 - 8 = 4 cm
VD = √VO² + OD²
= √(4√3)²+4²
= √16·3+16
= √64
VD = 8 cm (apotema bazei)
c) Al = Pb×ap/2
Pb = AB+BC+AC = 3×8√3 = 24√3cm
ap = VD = 8 cm
Al = 24√3×8/2 = 24×4×√3 = 96√3 cm²
d) V = Ab×h/3
Ab = l²√3/4 = AB²√3/4 = (8√3)²√3/4 = 64×3×√3/4 = 48√3 cm²
h = VO = 4√3 cm
V = 48√3×4√3/3 = 48×4×3/3 = 48×4 = 192 cm³
