Question

Calcule a área total e o volume de um prisma hexagonal regular de aresta da base 12 dm e altura 5 dm.​

Answer 1

Explicação passo-a-passo:

• Área total

$\sf A_t=2\cdot A_b+A_L$

$\sf A_t=2\cdot\dfrac{3\cdot12^2\sqrt{3}}{2}+6\cdot12\cdot5$

$\sf A_t=2\cdot\dfrac{3\cdot144\sqrt{3}}{2}+360$

$\sf A_t=2\cdot\dfrac{432\sqrt{3}}{2}+360$

$\sf A_t=432\sqrt{3}+360$

$\sf \red{A_t=72\cdot(6\sqrt{3}+5)~dm^2}$

• Volume

$\sf V=A_b\cdot h$

$\sf V=\dfrac{3\cdot12^2\sqrt{3}}{2}\cdot5$

$\sf V=\dfrac{3\cdot144\sqrt{3}}{2}\cdot5$

$\sf V=\dfrac{432\sqrt{3}}{2}\cdot5$

$\sf V=216\sqrt{3}\cdot5$

$\sf \red{V=1080\sqrt{3}~dm^3}$