Is there any way to prove that for any isosceles triangle, the volume of a solid created when that triangle is projected to a point determining the height above the angle opposite the hypotenuse is one third of the volume of a triangular prism of the same height and base shape?

![enter image description here](https://i.stack.imgur.com/fpA8N.png)

Here's a sketch. The projected solid can be thought of as one quarter of a square pyramid when N is 90 degrees. Is there a way to prove that the projected solid's volume is one third that of the triangular prism of same height and base values for any value of N?

Both intuitive and purely mathematical proofs are acceptable.