A triangular prism or a triangular based pyramid
You can call it a "triangular prism" rather than "triangular based prism" ... saying a prism is "triangular" imply that the base is a triangle. There's no other name that I know of. A prism is just a 3d shape, so all you have to say is <type of shape> + prism to get the point across.
Square based Triangular prism
it is called a triangular prism
A triangular prism can have a square or triangular base.
A triangular prism has a triangle and a rectangular prism doesn't.
A triangular prism has two triangular faces, a rectangular prism does not have any.
A triangular prism.
A triangular prism has a triangular cross-section. A rectangular prism has a rectangular cross-section.
A triangular prism has triangular bases, a heagonal prism has ... you guessed it! ... hexagonal bases.
It could be a triangular prism or a quadrilateral based pyramid.