Table of Contents

Last modified on August 3rd, 2023

A triangular prism is a three-dimensional solid consisting of two identical triangular bases joined together by three rectangular faces. The lateral faces are rectangular. A triangular prism has 5 faces (3 rectangular lateral faces and 2 triangular bases), 9 edges, and 6 vertices.

A common example of triangular prisms is prisms used in the physics lab for refracting white light. Other real-life examples are camping tents or chocolate candy bars.

A triangular** **prism can be **regular** or **irregular** based on the uniformity of its cross-section. It can also be **right** or **oblique**, depending on the alignment of its bases.

**Regular Triangular Prism**â€“ Its 2 bases are equilateral triangles.**Irregular Triangular Prism**– Its 2 bases are not equilateral triangles.

**Right Triangular Prism**â€“ It has all the lateral faces perpendicular to the bases. Thus every lateral face is rectangular.**Oblique Triangular Prism**â€“ Its lateral faces are not perpendicular to its bases. So, every lateral face is parallelogram-shaped.

Like all other polyhedrons, we can calculate the surface area and volume of a triangular prism.

The surface area of a triangular prism is the entire space occupied by its outermost layer (or faces). It is expressed in square units such as m^{2}, cm^{2}, mm^{2}, and in^{2}. It has 2 types of surface areas.

The lateral surface area (LSA) of a triangular prism is the sum of the surface area of all its faces except the bases. The formula to calculate the total and lateral surface area of a triangular prism is given below:

**Lateral Surface Area (****LSA****) = ( s_{1} + s_{2} + s_{3}) Ã— l, **here,

The total surface area (TSA) of a triangular prism is the sum of the lateral surface area and twice the base area. The formula to calculate the TSA of a triangular prism is given below:

**Total Surface Area ( TSA) = (b Ã— h) + (s_{1} + s_{2} + s_{3}) Ã— l**, here,

Let us solve some examples to understand the concept better.

**Find the surface area of a triangular prism with a triangular base of 7 cm, 6 cm, and 4 cm, and height 6 cm, and length 9 cm.**

Solution:

As we know,

Total Surface Area (*TSA*) = *b* Ã— *h* + (*s_{1} + s_{2} + s_{3}*) Ã—

âˆ´

= 189 cm

**Find the lateral and total surface area of a triangular prism with an equilateral triangular base of 6.5 cm, and length is 10.5 cm.**

Solution:

As we know,

The prism is an equilateral triangular prism, so height is not required,

Total Surface Area* (TSA) = 2B *+* (s _{1} *+

Applying the formula to find the area of an equilateral triangle,

âˆ´ Â

â‰ˆ 18.3 cm

Now,

= 241.35 cm

Lateral Surface Area

âˆ´ Â

= 204.75 cm

The volume of a triangular prism is its space in the three-dimensional plane. The formula to calculate the volume of a triangular prism is given below:

**Volume**** (V) = **** 1/2 Ã— b Ã— h Ã— l, **here

Let us solve an example to understand the concept better.

**Find the volume of a triangular prism whose base is 16 cm, height is 9 cm, and length is 21 cm.**

Solution:

As we know,

Volume (*V*) = 1/2 Ã— *b* Ã— *h* Ã— *l*, here *b* = 12 cm, *h* = height, *l* = 21 cm

âˆ´ Â *V* = 1/2 Ã— 16 Ã— 9 Ã— 21

= 1512 cm^{3}

**More Resources:**- Volume of a Prism
- Surface Area of a Prism
- Right Prism
- Oblique Prism
- Rectangular Prism
- Volume of a Rectangular Prism
- Surface Area of a Rectangular Prism
- Triangular Prism
- Volume of a Triangular Prism
- Surface Area of a Triangular Prism
- Hexagonal Prism
- Volume of a Hexagonal Prism
- Surface Area of a Hexagonal Prism
- Pentagonal Prism
- Volume of a Pentagonal Prism
- Surface Area of a Pentagonal Prism
- Trapezoidal Prism
- Volume of a Trapezoidal Prism
- Surface Area of a Trapezoidal Prism
- Square Prism
- Volume of a Square Prism
- Surface Area of a Square Prism
- Octagonal Prism
- Heptagonal Prism
- Decagonal Prism

Last modified on August 3rd, 2023