Question

Calcule a área lateral e o volume de uma pirâmide quadrangular regular, tendo a aresta da base medindo 8 cm e altura 10 cm.

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{h^2 = 10^2 + 4^2}$

$\mathsf{h^2 = 100 + 16}$

$\mathsf{h^2 = 116}$

$\mathsf{h^2 = 2^2.29}$

$\boxed{\boxed{\mathsf{h = 2\sqrt{29}\:cm}}}\leftarrow\textsf{altura do tri{\^a}ngulo da face}$

$\mathsf{A_L = \dfrac{4.B.h}{2}}$

$\mathsf{A_L = \dfrac{4.8.2\sqrt{29}}{2}}$

$\mathsf{A_L = 32\sqrt{29}}$

$\boxed{\boxed{\mathsf{A_L = 172,33\:cm^2}}}\leftarrow\textsf{{\'a}rea lateral}$

$\mathsf{V = \dfrac{A_B.h}{3}}$

$\mathsf{V = \dfrac{8^2.10}{3}}$

$\mathsf{V = \dfrac{64.10}{3}}$

$\mathsf{V = \dfrac{640}{3}}$

$\boxed{\boxed{\mathsf{V = 213,33\:cm^3}}}\leftarrow\textsf{volume}$