How many faces does a triangular prism have?

Complete step-by-step solution:
Let's discuss more about triangular prisms and we will draw pictures of triangular prisms to actually visualize the figure for better understanding.

There are a total of 5 faces and 9 edges.

Note: Triangular prism is mostly used in telescopes, periscopes and microscopes, scientists also use the triangular prism in studying the reaction of light with human eye, as prism is used to treat many human diseases which help redirect the light entering the eye to enhance the vision of the patient, also used in various vision correcting lenses.

We know that a triangular prism is a three-sided prism. It’s a polyhedron made of 2 triangular bases and 3 rectangular faces joining sides.

We observe that this triangular prism has 5 faces – 2 triangular bases and 3 rectangular faces joining sides. We observe that the triangular prism has 6 edges – A, B, C, D, E, and F.
We can now count the number of edges of the prism, or, we can use the formula $f+v-e=2$, where f denotes the number of faces, v denotes the number of vertices and e denotes the number of edges to count the number of vertices of the prism.
Substituting $f=5,v=6$ in the above formula, we have $5+6-e=2$.

Rearranging the terms, we have $e=11-2=9$.
Thus, the prism has 9 edges. We can also count these edges by looking at the prism.
Hence, the triangular prism has 5 faces and 9 edges.
Note: It’s difficult to count the number of edges on the prism from a diagram due to its 3 – D orientation. Thus, it’s better to use the relation given between the number of edges, vertices, and faces to count the number of edges of the prism.

A triangular prism has a triangle for the base. Every cross-section parallel to the base is also a triangle.

A net of a triangular prism is shown here.

A triangular prism has 5 faces, 6 vertices and 9 edges. To build a rectangular prism with construction materials, we would need 3 rectangles and 2 triangles that join at the edges to make a closed three-dimensional shape or 9 edge pieces and 6 corner pieces to make a frame of the prism.

Table of contents:

What is a Triangular Prism?

Triangular Prism 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 the triangular 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.

The sides and bases of the triangular prism are congruent or else oblique. The edges of the prism join the corresponding sides.  The two bases of this prism are equilateral triangles and the edges of these triangles are parallel to each other. See the below figure to understand the structure.

Other Types of Prisms

• Rectangular Prism
• Square prism
• Pentagonal 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 are 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

Right Triangular Prism

A right triangular prism has its three rectangular sides congruent. Also, the two triangular bases are parallel and congruent to each other. The rectangular or lateral faces are perpendicular to the triangular bases.

Volume 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. The formula to find the volume of triangular prism is given by:

Volume = Area of the Base × Height of prism

Since, the base is in triangular shape, therefore,

Area = ½ b h

Hence,

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

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. The formula of surface area of triangular prism is given by:

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 triangular base= ½ × b × h

If 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

Surface 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.

Triangular Prism Net

If we open each face of the triangular prism, we will get the net. The net of this prism comprises three rectangles and two triangles. In the below figure you can see the nine distinct nets.

Facts to Remember

• Number of faces = 5
• Number of edges = 9
• Number of vertices = 6
• Shape of the base = Triangular
• Shape of Sides = Rectangular or Square
• Surface Area = 2(Area of triangular bases) + Perimeter of base x Height of prism
• Volume = Area of base x Height of Prism

Related Articles

• Area Of prism
• Volume of a Prism

Solved Examples on 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 cm3

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 + (18)4) = 50 + 72

= 122 cm2

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Frequently Asked Questions on Triangular Prism