Question

o piramida patrulatera regulata VABCD are toate muchile egale . daca AB =6 cm atunci aria laterala a piramidei are.........cm la a 2

Answer 1

VABCD = piramida patrulatera regulata
Toate muchiile sunt congruente =) fetele laterale sunt triunghiuri echilaterale

Construiesc apotema piramidei VM, M ∈ BC , BM = MC = AB/2 = 6/2 = 3
VM = inaltime in fata laterala VBC =) VM = (l√3)/2 = (6√3)/2 = 3√3
VM = 3√3 cm

Baza = patrat =) Pb = 4l = 4×6=24

Aria laterala = (Pb × ap ) / 2 = (24 × VM ) / 2 = 12 × 3√3 = 36√3 cm²