triangle
A triangular prism has a uniformed cross-section whereas a rectangular pyramid does not.
a triangular pyramid
A solid with a triangular cross section when the cross section is taken parallel to the base could be either a triangular prism, a triangular pyramid, or a triangular frustrum.. I've been sitting here trying to convince myself (without actually bearing down and trying to prove it mathematically) that any cross section of a regular tetrahedron (a special case of triangular pyramid) taken perpendicularly to the base is a triangle, and I THINK this is the case, but as I said I certainly haven't rigorously proven it; I'm just unable to come up with any obvious situation where this is not true.
The cross section of a pyramid shrinks from the shape of the base down to a point as you move along its axis from the base to the apex. The cross section of a prism is constant along its axis.
Yes. A cuboid, for example, has triangular cross sections
The horizontal cross section of a triangular pyramid, or tetrahedron, is a shape that varies depending on the height at which the section is made. At different heights, the cross section will be a triangle, with its size and proportions changing as you move up or down the pyramid. If the section is made at the base, the cross section will equal the triangular base itself, while sections taken higher up will be smaller triangles. The shape remains triangular throughout, but its dimensions shrink as you ascend towards the apex.
A triangular prism has a uniformed cross-section whereas a rectangular pyramid does not.
A prism can have a triangular cross-section with a rectangular base
Pyramid, triangular prism, cone.
a triangular pyramid
A solid with a triangular cross section when the cross section is taken parallel to the base could be either a triangular prism, a triangular pyramid, or a triangular frustrum.. I've been sitting here trying to convince myself (without actually bearing down and trying to prove it mathematically) that any cross section of a regular tetrahedron (a special case of triangular pyramid) taken perpendicularly to the base is a triangle, and I THINK this is the case, but as I said I certainly haven't rigorously proven it; I'm just unable to come up with any obvious situation where this is not true.
cone, cylinder, rectangular prism, square pyramid and triangular prism
A triangular prism has a triangular cross-section. A rectangular prism has a rectangular cross-section.
The vertical cross section of a square pyramid is a triangle. When the pyramid is sliced vertically through its apex and down to the base, the resulting shape is a triangular profile that includes the apex at the top and the edges of the base at the bottom. The height of the triangle corresponds to the height of the pyramid, while the base of the triangle spans the width of the base of the pyramid.
A cross section of a rectangular pyramid through its vertex and perpendicular to its base creates a triangular shape. This triangle's base corresponds to one of the edges of the rectangular base, while its apex is at the vertex of the pyramid. The height of the triangle is determined by the vertical distance from the vertex to the base.
The cross section of a pyramid shrinks from the shape of the base down to a point as you move along its axis from the base to the apex. The cross section of a prism is constant along its axis.
When a square pyramid is sliced perpendicular to its base through a vertex, the cross section will be a triangle. This triangle will have one vertex at the apex of the pyramid and the other two vertices on the base, forming a triangular shape that includes one of the pyramid's edges and a segment of the base. The resulting triangle will be isosceles if the slice is made symmetrically.