Question

find the volume of this oblique prism. the base is a hexagonal prism. the perimeter is 36. height is 15.

Answer 1

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:

`(3√(3))/(2)s^2`

where (s) is the side length of the hexagon

So, the volume of the prism will be as follows:

`volume=(3√(3))/(2)s^2h`

substitute s = 6, and h = 15

`volume=(3√(3))/(2)*6^2*15=810√(3)`

So, the answer will be:

The volume of the given prism = 810√3 cubic units