Question

Intr-o piramida triunghilara regulata latura bazei are 10 radical din 3 cm , iar inaltimea 12 cm .Determinati lungimea apotemei bazei . Va rooog , cat mai repede daca se poate ! ^^

Answer 1

Consideram
VABC-piramida triunghiulara regulata unde
ΔABC-Δechilateral AB=10√3cm;
VO⊥(ABC) ,VO=12cm;
Construim AM⊥BC ,M∈(BC)
[AM]=h ⇒AM=AB√3/2 ⇒AM=15cm
O∈(AM) ⇒AO+OM=AM=15cm
OM=AM/3 ⇒OM=5cm
VO⊥(ABC)
AM⊥BC
AM,BC⊂(ABC)
AM∩BC={M} ⇒T₃⊥ VM⊥BC ⇒d(V;BC)=VM=apotema piramida;
Aplicam T.P. in ΔVOM m(<O)=90 de grade ⇒
VM=√VO²+OM²=√12²+5²=√144+25=√169=13
VM=13cm⇒apotema piramida=13cm;
Apotema bazei=OM=5cm.