Question

Seja a pirâmide quadrangular regular cuja altura mede h = 3 cm e área da base é igual a 64 cm2 Calcular:

a) O apótema da pirâmide,
b) área lateral,
c) área total
d) o volume

Answer 1

cálculo da aresta da base:

$\mathsf{B=\ell^2}\\\mathsf{\ell^2=64}\\\mathsf{\ell=\sqrt{64}=8~cm}$

cálculo do apótema da base:

$\mathsf{m=\dfrac{\ell}{2}=\dfrac{8}{2}=4~cm}$

a)

$\mathsf{a_{p}^2=h^2+m^2}\\\mathsf{a_{p}^2=3^2+4^2}\\\mathsf{a_{p}^2=9+16=25\to~a_{p}=\sqrt{25}}\\\large\boxed{\boxed{\boxed{\boxed{\mathsf{a_{p}=5~cm}}}} </p><p>}$

b)

$\mathsf{A_{L}=4.\dfrac{1}{2}.8.5=80~cm^2}$

c)

$\large\boxed{\boxed{\boxed{\boxed{\mathsf{A_{t}=64+80=144~cm^2}}}}}$

d)

$\large\boxed{\boxed{\boxed{\boxed{\mathsf{V=\dfrac{1}{3}.64.3=64~cm^3}}}}}$