Question

Piramida triunghiulara regulata VABC are inaltimea VO=6cm si latura bazei AB=18cm,Calculati d(C,(VAB))

Answer 1

Fie VL⊥AB

T∈VL a.i.CT⊥Vl

T⊂(VAB)

d(C,(VAB)=CT

V=Ab*h/3

fie VN⊥BC si AN⊥BC

BN=BV/2=AB/2=18/2=9 cm

In ΔANB , m(∡N)=90°=>AN²=AB²-BN²=18²-9²=324-81=243=>AN=√243=9√3 cm

Ab=AN*BC/2=9√3*18/2=81√3 cm²

V=Ab*h/3=81√3*6/3=162√3 cm³

ON=AN/3=9√3/3=3√3 cm

In ΔVNO , m(∡O)=90°=>VN²=VO²+ON²=6²+(3√3)²=36+27=>VN=√63=3√7 cm

VN=VL=3√7 cm

A_VAB=AB*VL/2=18*3√7/2=27√7 cm²

V=A_VAB*CF/3<=>162√3=27√7CF/3<=>162√3=9√7CF=>CF=18√21/7 cm