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In geometry, a triangular prism or three-sided prism is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.
If the sides are squares, it is called a uniform polyhedron. In general the sides can be congruent rectangles.
Equivalently, it is a pentahedron of which two faces are parallel, while the surface normals of the other three are in the same plane (which is not necessarily parallel to the base planes). These three faces are parallelograms. All cross-sections parallel to the base faces are the same triangle.
A right triangular prism is semiregular if the base faces are equilateral triangles, and the other three faces are squares.
A general right triangular prism can have rectangular sides.
The dual of a triangular prism is a 3-sided bipyramid.
The symmetry group of a right 3-sided prism with regular base is D3h of order 12. The rotation group is D3 of order 6.
The symmetry group does not contain inversion.
Surface area and volume of a triangular prism
To get the surface area of a triangular prism, you need to find the base area(0.5*bh) of the triangle. This is known as A1 in the following formula. The rectanges are known as A2, A3, and A4 in this formula.
The formula for an equilateral triangular base in the prism is:
- A1×2+A2×3
- A1×2+A2×2+A3
- A1×2+A2+A3+A4
To get the volume of a triangular prism you need to find the base area of the triangle(0.5*bh) and the length of the prism.
The formula is: Base Area*length or 0.5*base*height*length
See also
- Set of prisms
- Cube Square-capped prism
- Pentagonal prism
- Hexagonal prism
External links
- Paper model triangular prism Prism nets
"Triangular prism"