Question

VABC este o piramida triunghiulara regulata cu apotema bazei OM=3cm si inaltimea piramidei VO=3√3.
a)Calculati aria laterala a piramidei.
b)Determinati volumul piramidei.

Answer 1

Al=Pb·ap/2
ap²=h²+ab²
ap²=27+9
ap=√36=6cm
OM=1/3·BM
3=1/3·BM
BM=9cm
AB=18cm
P=3l=3·18=54cm
Al=54·6/2
Al=162cm²
V=Ab·h/3
Ab=l²√3/4⇒324√3/4=81√3cm²
V=81√3·3√3/3=243cm³

Answer 2

Al=Pb·ap/2
ap²=h²+ab²
ap²=27+9
ap=√36=6cm
OM=1/3·BM
3=1/3·BM
BM=9cm
AB=18cm
P=3l=3·18=54cm
Al=54·6/2
Al=162cm²
V=Ab·h/3
Ab=l²√3/4⇒324√3/4=81√3cm²
V=81√3·3√3/3=243cm³