Hello, reiward!

Find the volume of an oblique triangular prism

whose base is an equilateral triangle with side 12 cm.

The lateral edge of the prism is also 12 cm,

and is inclined to the base at an angle of 30°.

The volume of a pyramid is: .

. . where: . = area of base, and = height.

The area of an equilateral triangle of side is: .

. . Hence, our pyramid has base area: .

Look at a cross-section of the pyramid. Code:

*
*| *
* | *
* | * 12
* |h *
* | *
* | *
* | 30° *
* * * * * * * * *

And we see that: .

Therefore: .