Answer:
The volume of the hexagon is equal to [tex]3,240\sqrt{3}\ units^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the prism is equal to
[tex]V=BH[/tex]
where
B is the area of the base of the prism
H is the height of the prism
we have
[tex]H=15\ units[/tex]
To find the area of the base (hexagon) calculate the area of one equilateral triangle and then multiply by 6
[tex]A=\frac{1}{2}bh[/tex]
we have
[tex]b=12\ units[/tex]
Applying Pythagoras theorem calculate the height of the triangle
[tex]h^{2}=12^{2}-6^{2}[/tex]
[tex]h^{2}=144-36[/tex]
[tex]h^{2}=108[/tex]
[tex]h=\sqrt{108}=6\sqrt{3}\ units[/tex]
substitute
The area of one triangle is equal to
[tex]A=\frac{1}{2}(12)(6\sqrt{3})[/tex]
[tex]A=36\sqrt{3}\ units^{2}[/tex]
Find the volume of the prism
[tex]V=6*36\sqrt{3}*15=3,240\sqrt{3}\ units^{3}[/tex]
