Question

Calcule a área e o volume da pirâmide de base:

A- quadrada de altura 25 cm e aresta da base 5 cm.
B- Hexagonal de aresta da base 5 cm e apótema da pirâmide 25 cm.

Answer 1

volume dá pirâmide quadrada
V= volume
Ab= área dá base
h= altura

V= (1/3).Ab.h
V= (1/3).25.25
V= 208,33 cm^3

hexagonal

Ab= (3.a^2.√3)/2
Ab= (3.5^2.√3)/2
Ab= 64,95 Cm^2

V= (1/3).Ab.h
V= (1/3).64,95.25
V= 541,25Cm^3

Answer 2

Caso esteja pelo app, e tenha problemas para visualizar esta resposta, experimente abrir pelo navegador https://brainly.com.br/tarefa/9333574

                                                                                                                               

$\sf~\tt a)~\sf m=\dfrac{5}{2}=2,5~cm\\\sf a_p^2=625+\left(\dfrac{5}{2}\right)^2\\\sf a_p^2=625+\dfrac{25}{4}\\\sf a_p^2=\dfrac{2500+25}{4}\\\sf a_p^2=\dfrac{2525}{4}\implies a_p=\dfrac{5\sqrt{101}}{2}~cm\\\sf A_l=\diagup\!\!\!4\cdot\dfrac{1}{\diagup\!\!\!2}\cdot5\cdot\dfrac{5\sqrt{101}}{\diagup\!\!\!2}\\\sf A_l=25\sqrt{101}~cm^2\\\sf B=5^2=25~cm^2\\\sf A_t=A_l+B\\\sf A_t=25\sqrt{101}+25\\\huge\boxed{\boxed{\boxed{\boxed{\sf A_t=25(\sqrt{101}+1)~cm^2}}}}$

$\sf V=\dfrac{1}{3}\cdot25\cdot 25\\\huge\boxed{\boxed{\boxed{\boxed{\sf V=\dfrac{625}{3}~cm^3}}}}$

$\tt b)~\sf m=\dfrac{5\sqrt{3}}{2}\\\sf a_p^2=h^2+m^2\\\sf 25^2=h^2+\left(\dfrac{5\sqrt{3}}{2}\right)^2\\\sf 625=h^2+\dfrac{25\cdot3}{4}\\\sf 4h^2+75=2500\\\sf 4h^2=2500-75\\\sf 4h^2=2425\\\sf h^2=\dfrac{2425}{4}\\\sf h=\sqrt{\dfrac{2425}{4}}\implies h=\dfrac{5\sqrt{97}}{2}~cm$

$\sf A_l=\diagup\!\!\!6^3\cdot\dfrac{1}{\diagup\!\!\!2}\cdot 5\cdot25\\\sf A_l=375~cm^2\\\sf B=\dfrac{1}{2}\cdot5^2\cdot\dfrac{5\sqrt{97}}{2}\\\sf B=\dfrac{125\sqrt{97}}{4}~cm^2\\\sf A_t=A_l+B\\\boxed{\sf A_t=375+\dfrac{125\sqrt{97}}{4}~cm^2}\\\sf V=\dfrac{1}{3}\cdot\dfrac{125\sqrt{97}}{4}\cdot 25\\\boxed{\sf V=\dfrac{3125\sqrt{97}}{12}~cm^3}$