Răspuns:
Explicație pas cu pas:
AB=12cm, ap=DM=6√3cm.
a) Al=Pb·ap=3·AB·DM=3·12·6√3=216√3cm².
b) V=(1/3)·Ab·h,
Ab=AB²·√3/4=12²·√3/4=36√3 cm².
AB=AO·√3, ⇒AO·√3=12 ⇒AO=12/√3=12√3/3=4√3 cm=BO. Atunci OM=(1/2)BO=2√3.
Din ΔDOM , DO²=DM²-OM²=(6√3)²-(2√3)²=(6√3-2√3)(6√3+2√3)=4√3·8√3=32·3=16·6, ⇒DO=√(16·6)=4√6cm=h.
Deci V=(1/3)·36√3·4√6=48√18=48√(9·2)=48·3√2=144√2cm³
