A hexagonal prism.
A hexahedron or a triangular dipyramid. This is the shape formed by two triangular pyramids (tetrahedrons) stuck together along one triangular face.
sqare based pyramid
There is no such shape - unless there are other faces. If there is one rectangular face then you require at least four other faces - one on each edge of the rectangle - making a minimum of 5 faces.
It have six (as in hexagonal) around the edge, a top and bottom face and the hole in the middle with the thread. So it have 8 faces.
A cuboid prism has no triangular faces
The solid shape that has one square face and four triangular faces is called a pyramid. If you were to have a shape that had four triangular faces and no square face, it would be called a triangular pyramid.
An octahedron is a closed 3-d shape with 8 polygonal faces. There are 257 topologically different convex octahedra. An octahedron can have triangles for all eight faces or, as is the case with a hexagonal prism, not a single triangular face.
An octagon is a plane shape with just one face - an octagonal face! It cannot have triangular faces.
A 10-sided die has 10 triangular faces.
A hexagonal prism.
Triangular prisim
There is no 3-d shape with 4 and 1 = 5 triangular faces.
If the base of the pyramid is a triangle then all its faces would be triangular in shape.
The shape you are describing is a triangular pyramid. A triangular pyramid has a base that is a triangle and three triangular faces that meet at a single point called the apex. The base of the pyramid is a rectangle, which is a quadrilateral with four right angles. The triangular faces of the pyramid connect the vertices of the base to the apex.
A hexahedron or a triangular dipyramid. This is the shape formed by two triangular pyramids (tetrahedrons) stuck together along one triangular face.
A square based pyramid.