# Triangular Prism

A **triangular prism** is a polyhedron, made up of two triangular bases and three rectangular sides. By the definition, the two triangular bases are parallel and congruent to each other. It is a pentahedron and has nine distinct nets. The **edges and vertices** of the bases are joined with each other via three rectangular sides. The sides of this prism, which are rectangular in shape are joint with each other side by side. All cross-sections parallel to the base faces are the same as a triangle. A **triangular pyramid** has four triangular bases unlike the triangular prism, joined with each other and all are congruent to each other.

Prism is a three-dimensional shape made up of at least three flat surfaces. In geometry, you will come across different types of prism such as Triangular Prism, Rectangular Prism, Polygonal Prisms, etc. You can also consider Cubes and Cuboid as examples of Prism. These prisms are usually made up of transparent materials such as Glass, Plastic, etc.

## Triangular Prism Definition

In geometry, a triangular prism is a prism with three sides, which has two triangular bases and three edges. The sides of this prism are in rectangular shape or else it is oblique. The edges of the prism joins the corresponding sides. The two bases of this prism are equilateral triangles and edges of these triangles are parallel to each other. See the below figure to understand the structure.

## Volume and Surface Area of Triangular Prism

The volume of a triangular prism is equal to the product of the triangular base area and the height of the prism.

Volume = Area of the Base × Height of prism

Volume of Triangular Prism = ½ × b × h × l |

Where b is the base length, h is the height of the triangle and l is the length between the triangular bases.

Surface area of triangular prism is equal to the sum of the lateral surface area and twice the base area of the triangular prism. It is measured in square units.

Surface area of triangular prism = 2A + PH

Where A is the area of the triangular bases, P is the perimeter of the bases and H is the height of the prism.

Now, Area of the base= ½ × b × h

If suppose, a, b and c are the sides of the triangular bases, then,

Perimeter of the base = a + b + c

Therefore,

Surface area of triangular prism = 2(½ × b × h) + ( a + b + c)H

Area of the Triangular Prism = (bh + ( a + b + c)H) |

Where b and h is the base and height of the bases, respectively and H is the height of the prism.

## Properties of Triangular Prism

Let us discuss some of the properties of the triangular prism.

- It has a total of 9 edges, 5 faces, and 6 vertices(which joined by the rectangular faces).
- It has two triangular bases and three rectangular sides.
- If the triangular bases are equilateral and the other faces are squares, instead of a rectangle, then the triangular prism is said to be semiregular.

## Examples of Triangular Prism

**Example 1: Find the volume of the triangular prism with base is 5 cm, height is 10 cm, and length is 15 cm.**

**Solution:** Volume of Triangular Prism = ½ × b × h × l

V = ½ × 5 × 10 × 15

Volume, V = 375 cm^{3}

**Example 2: If the height of the prism is 4cm and the length of the side of the equilateral triangular base is 6cm. Then find the area of the prism for the above example.**

**Solutions: **We have,

Base = 5cm, height of the base= 10cm, length of the base=15cm, Height of the prism = 4cm

As the base is an equilateral triangle, therefore all its sides will be equal.

Hence, a = b = c = 6cm.

By the formula,

Area of the Triangular Prism = (bh + ( a + b + c)H)

Area = (5 × 10+(6+6+6)4) = (50+(24)4) = 50+96 = 146 cm^{2}