Question

Prisma hexagonal
(com resoluçao)
Calcule:

> area lateral
> area de uma base
> area total
> diagonal D

obg

Answer 1

$\boxed{\begin{array}{l}\sf A_{lateral} =6\cdot2\cdot3=36~u\cdot a\\\sf A_{base} =\dfrac{3\cdot2^2\sqrt{3}}{2}=6\sqrt{3}~u\cdot a\\\sf A_{total}=A_{lateral} +2A_{base}\\\sf A_{total} =36+2\cdot6\sqrt{3}\\\sf A_{total}=36+12\sqrt{3}\\\sf A_{total} =12\cdot(3+\sqrt{3})~u\cdot a\end{array}}$

$\boxed{\begin{array}{l}\underline{\rm diagonal~do~hex\acute agono:}\\\sf d=2\cdot2=4~u\cdot c\\\underline{\rm diagonal~do~prisma:}\\\sf D^2=d^2+h^2\\\sf D^2=4^2+3^2\\\sf D^2=16+9\\\sf D^2=25\\\sf D=\sqrt{25}\\\sf D=5~u\cdot c \end{array}}$