Answer:
See Explanation
Step-by-step explanation:
The question is incomplete, as the dimensions of the hexagon are not given.
I will assume that:
[tex]b = 6[/tex] --- base length
[tex]h = 8[/tex] --- height
First, we calculate the height (a) of each triangle that makes the hexagonal base
The formula to use is:
[tex]a^2 = b^2 - (\frac{b}{2})^2[/tex]
[tex]a^2 = 6^2 - (\frac{6}{2})^2[/tex]
[tex]a^2 = 6^2 - (3)^2[/tex]
[tex]a^2 = 36 - 9[/tex]
[tex]a^2 = 27[/tex]
Take positive square roots
[tex]a = \sqrt{27[/tex]
Expand
[tex]a = \sqrt{9*3[/tex]
Split
[tex]a = \sqrt{9}*\sqrt3[/tex]
[tex]a = 3\sqrt3[/tex]
So, we have:
[tex]Area = \frac{1}{2}ap[/tex]
Where
[tex]a = 3\sqrt3[/tex]
[tex]p =perimeter[/tex]
[tex]p = 6 * b[/tex] ---- 6 represents the sides of the hexagon
[tex]p = 6 * 6[/tex]
[tex]p = 36[/tex]
[tex]B= \frac{1}{2}ap[/tex]
[tex]B= \frac{1}{2} * 3\sqrt 3 * 36[/tex]
[tex]B= 3\sqrt 3 *18[/tex]
[tex]B = 54\sqrt 3[/tex]
[tex]h = 8[/tex]
Lastly, the volume is:
[tex]V = \frac{1}{3}Bh[/tex]
So:
[tex]V = \frac{1}{3} * 54\sqrt3 * 8[/tex]
[tex]V = 18\sqrt3 * 8[/tex]
[tex]V = 144\sqrt3[/tex]
