Question

Calcule a área e volume de um prisma de base hexagonal de altura 12 cm e aresta da base igual a 3 cm

Answer 1

$\textup{ A area hexagono regular é a soma de 6 triangulos equilateros}\newline\textup{fica 6 vezes area triangulo equilatero}\\\textup{a altura do triangulo equilatero }h^2+(\frac{a}{2})^2=a^2\\ \Rightarrow h^2=a^2-\frac{a^2}{4}=\frac{3a^2}{4}\Rightarrow\\ h=\frac{\sqrt{3}a}{2} \textup{a area do triangulo equilatero e } A=\frac{b.h}{2}= \frac{3^2.\sqrt{3}}{4}=\frac{9.\sqrt{3}}{4} \\ A_{base}=6.A=6.\frac{9.\sqrt{3}}{4} =\frac{54.\sqrt{3}}{4} \\ V_{prisma}=A_{base}.h=\frac{54.\sqrt{3}}{4} .12\\V_{prisma}=162.\sqrt{3}cm^3$