Difference Between Triangular Prism and Triangular Pyramid (Tetrahedron)

Triangular Prism vs Triangular Pyramid (Tetrahedron)

In geometry, a polyhedron is a geometric solid in three dimensions with flat faces and straight edges. A prism is a polyhedron with an n-sided polygonal base, an identical base on another plane and no other parallelograms joining corresponding sides of the two bases.

A pyramid is a polyhedron formed by connecting a polygonal base and a point, which is known as the apex. The base is a polygon and the sides of the polygon are connected to the apex through triangles.

Triangular Prism

A triangular prism is a prism with triangles as its base; i.e. the cross sections of the solid parallel to the bases are triangles at any point within the solid. It also can be considered as a pentahedron with two of the sides parallel to each other, while the surface normal to the three other surfaces lies in the same plane (a plane that is different from the base planes). The sides other than the bases are always rectangles.

The prism is said to be a right prism if the planes of the bases are perpendicular to the other surfaces.

The volume of the prism is given by

Volume = base area × height

It is the product of the area of the base triangle and the length between the two bases. 

Triangular Pyramid (Tetrahedron)

A triangular pyramid is a solid object consisting of triangles in all four sides. It is the simplest type of the pyramids. It is also known as the tetrahedron, which also is a type of polyhedrons.

It can also be considered as a solid object formed by joining the lines from the vertices of a triangle at a point above the triangles. In this definition, the faces of the tetrahedron can be different triangles. However, the often encountered case is the regular tetrahedron, which has equilateral triangles as its sides.

The volume of the tetrahedron can be obtained using the following formula.

Volume = (1/3) base area × height

Here the height refers to the normal distance between the base and the apex.

Since its figure directly forms from the triangles, the tetrahedrons display many analogous properties of triangles, such as circumsphere, insphere, exspheres, and medial tetrahedron. It has respective centers such as circumcenter, incenter, excenters, Spieker center, and points such as a centroid.

What is the difference between Triangular Prism and Triangular Pyramid (Tetrahedron)?

• Both triangular prism and triangular pyramid (Tetrahedron) are polyhedrons, but the triangular prism consists of triangles as the base of the prism with rectangular sides, whereas the tetrahedron consists of triangles at every side.

• Therefore, triangular prism has 5 sides, 6 vertices and 9 edges while tetrahedron has 4 sides, 4 vertices and 6 edges.

• The cross sectional area along the axis through the bases does not change in the triangular prism, but in the tetrahedron the cross sectional area changes (decreases with the distance from the base) along the axis perpendicular to the base.

• If the tetrahedron and the triangular prism have the same triangle as the base and the same height, the volume of the prism is three times the volume of the tetrahedron.