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Maths > Triangular Prism
Maths

Triangular Prism

In the geometry, the prism is a common shape having several varieties. Based on the base of it, it has many variations. One of such prism is the triangular prism. It is a three-sided prism. It is also termed as a polyhedron which has a triangular base. A uniform triangular prism is very common and it is the right triangular prism with equilateral bases and square sides. In this article, the student will learn about triangular prism, related terms as well as some important formulae. Let us begin it!

Triangular Prism Definition

A triangular prism is a popular polyhedron. It is having two triangular bases and three rectangular sides. According to the nature of prism, the two triangular bases are parallel and congruent to each other. It is a pentahedron with nine distinct nets. The edges and vertices of the bases are connected with each other. The rectangular sides of this prism are rectangular in shape and are joint with each other side by side. All the cross-sections parallel to the base faces are triangle.

triangular prism

Source: commons.wikimedia.org

The net of a solid figure is possible when a solid figure is unfolded along its edges and further its faces are laid out in a pattern in two dimensions. The net of a triangular prism is made up of rectangles and triangles. Also, the number of triangular prism edges is 9.

Volume and Surface Area of Triangular Prism:

Prism formula includes two very important formulae. These are Prism volume and Area of prism formulae. The volume of a prism is the space within the triangular prism. The surface area of a triangular prism is the amount of covered space on the outside surface of the prism. For these computations, we need the height, side and base length of the prism.

The volume of Triangular Prism Formula:

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

The volume of Prism = Area of the Base × Height of prism

Mathematically,

V = \(\frac {1}{2} \times b \times h \times l \)

V The volume of the prism
b Base length
h Height of the triangle
l Length of the prism

Surface Area of Triangular Prism Formula:

The surface area of a triangular prism is computed as the sum of the lateral surface area and base areas of both triangle bases. Thus,

The surface area of triangular prism = Lateral Area + 2 times the triangular base area

Mathematically,

  1. A. = P × H + 2 times A
S.A. The surface area of the prism
A Area of the base
P the perimeter of the base
H height of the prism

Area of triangle Formula:

A = \(\frac {1}{2} \times b \times h\)

A area of the triangle
h Height of triangle
b The base length of the triangle

The perimeter of the Base Formula:

Perimeter = a + b + c

Perimeter The perimeter of the triangle
a,b,c Three sides of the triangle

Solved Examples for You

Q.1: Find out the volume of the triangular prism with base length 10 cm, the height of 20 cm, and length of the prism as 50 cm.

Solutions: Parameters given in the problem,

b = 10 cm

h = 20 cm

l = 50 cm

Volume of the prism will be:

V = \(\frac {1}{2} \times b \times h \times l\)

Substituting the values,

V = \(\frac {1}{2} \times 10 \times 20 \times 50\)

V = \(\frac{1}{2} \times 10000\)

= 5000 \(cm^{3}\)

Thus volume of the triangular prism will be 5000 \(cm^{3}.\)

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