Given:
An oblique prism. the base is a hexagonal prism. the perimeter is 36.
The volume of the prism = base area * height
The base is hexagonal with a perimeter of 36
So, the side length = 36/6 = 6
the area of the hexagon is given by the following formula:
[tex]\frac{3\sqrt{3}}{2}s^2[/tex]where (s) is the side length of the hexagon
So, the volume of the prism will be as follows:
[tex]volume=\frac{3\sqrt{3}}{2}s^2h[/tex]substitute s = 6, and h = 15
[tex]volume=\frac{3\sqrt{3}}{2}*6^2*15=810\sqrt{3}[/tex]So, the answer will be:
The volume of the given prism = 810√3 cubic units
