Question

Fie piramida patrulatera VABCD de varf V si baza ABCD. Daca toate muchiile piramidei sunt congruente si egale cu 5cm, atunci aflati aria laterala si aria totala a piramidei.

Answer 1

Daca VABCD are toate muchiile congruente, atunci VABCD = tetraedru regulat

Perimetrul bazei = 4L = 4*5 = 20cm
Apotema piramidei = inaltime in fata laterala VBC (triunghi echilateral) =) VM = (l√3) / 2 = (5√3) / 2
Aria bazei = l² = 5² = 25 cm²

Aria laterala = (Pb * ap) / 2
Aria laterala = [20*(5√3)/2] / 2
Aria laterala = [(100√3)/2] / 2
Aria laterala = 50√3 / 2
Aria laterala = 25√3

Aria totala = Ab+Al = 25√3 +25 = 25(√3+1)cm²