Triangular prism
A triangular prism is a prism with triangular bases. In the figure below are three types of triangular prisms.
Properties of a triangular prism
A triangular prism is a polyhedron that has two parallel and congruent triangles called bases. The lateral faces (sides that are not bases) are parallelograms, rectangles, or squares. There are three lateral faces for a triangular prism. An edge is a line segment formed by the intersection of two adjacent faces. A vertex is the point of intersection of three edges.
Triangular prisms, like the one above, have a total of 5 faces, with 2 bases and 3 lateral faces. It also has 9 edges and 6 vertices.
Any cross section of a triangular prism that is parallel to the bases forms a triangle that is congruent to the bases.
Two triangular cross sections for the triangular prism are shown in green above. They are congruent to the two triangular bases of the triangular prism since they are formed by cross sections that are in planes parallel to the bases. This is true for any parallel cross section of a triangular prism.
Classifying triangular prisms based on their intersecting faces
Triangular prisms can be classified based on how their bases and lateral faces intersect or meet. If the bases are perpendicular to the lateral faces, meaning they meet at right angles, it is a right triangular prism. Otherwise it is an oblique triangular prism.
| Right triangular prism | Oblique triangular prism |
|---|---|
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Regular and irregular triangular prisms
Triangular prisms can also be classified based on the type of triangle that forms its base. A regular prism is defined by a prism whose bases are regular polygons. Therefore, if the bases of the triangular prism are equilateral triangles, it is a regular triangular prism. Otherwise it is irregular. Often, a regular triangular prism is implied to be a right triangular prism.
| Regular triangular prism | Irregular triangular prism |
|---|---|
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Volume of a triangular prism
The volume, V, of a triangular prism is the area of one of its bases times its height:
S = B·h
where B is the area of a triangular base and h is the height (the distance between the two parallel bases) of the triangular prism.
