Question

Num prisma triangular regular, a área da base é 4 raiz de 3 cm^2 e a área lateral é de 36cm^2. Calcule o volume

Answer 1

Olá.

$V = A_{base}.H\\\\\\ A_{base} = 4\sqrt3cm^2\\\\ A_{base} = \frac{L^2\sqrt3}{4}\\\\ 4\sqrt3 = \frac{L^2\sqrt3}{4}\\\\ 16\sqrt3 = L^2\sqrt3\\\\ L^2 = \frac{16\sqrt3}{\sqrt3}\\\\ L = \sqrt{16}\\\\ L = 4cm\\\\\\ A_{lateral} = 36cm^2\\\\ A_{lateral} = L.H\\\\ 36 = 4.H\\\\ H = 9cm\\\\\\ V = A_B.H\\\\ V = (4\sqrt3).9\\\\ V = 36\sqrt3$