A triangular prism is a polyhedron, (three-dimensional shape) consisted of of 2 triangular bases and three rectangle-shaped sides. Like other Prisms, the two bases right here are parallel and congruent to each other. It has 5 faces, 6 vertices and also 9 edges in total.

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Triangular Prism is a pentahedron and also has nine distinct nets. The edges and also vertices the the bases are joined v each various other via three rectangular sides.


Facts:Number of deals with = 5Number of edges = 9Number the vertices = 6Shape of the basic = TriangularShape of political parties = RectangularSurface Area = 2(Area of triangular bases)+Perimeter of basic x elevation of prismVolume = Area of basic x height of Prism

The political parties of triangular prism, i m sorry are rectangle-shaped in form are joint through each other side by side. Every cross-sections parallel to the base faces are the very same as a triangle. A triangular pyramid has 4 triangular bases unlike the triangle prism, joined through each other and also all are congruent to every other.


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Definition

In geometry, a triangle prism is a type of prism with three sides and also two bases. The sides room of rectangle shape and also bases are of triangle shape. Altogether, that has five faces, ripe vertices and six edges. 

The sides and bases of the triangle prism room congruent or rather oblique. The edges of the prism sign up with the corresponding sides. The 2 bases of this prism room equilateral triangles and edges of these triangles space parallel to every other. View the listed below figure to recognize the structure.

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Other species of Prisms

Right triangle Prism

A ideal triangular prism has actually its three rectangular sides congruent. Also, the two triangular bases are parallel and also congruent to every other. The rectangle-shaped or lateral encounters are perpendicular come the triangular bases.

Volume

The volume that a triangle prism is same to the product the the triangular basic area and also the elevation of the prism.


Volume = Area of the base × height of prism

Since, the base is in triangular shape, therefore,

Area = ½ b h

Hence,


Volume of triangle Prism = ½ × b × h × l

Where b is the basic length, h is the height of the triangle and also l is the length in between the triangle bases.

Surface Area

Surface area of triangle prism is same to the amount of the lateral surface area and also twice the base area that the triangle prism. That is measured in square units.


Surface area of triangle prism = 2A + PH

Where, 

A is the area of the triangle bases, P is the perimeter the the bases and H is the elevation of the prism

Now, Area the the triangular base= ½ × b × h

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

Perimeter the the basic = a + b + c

Therefore,

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


Surface Area the the triangular Prism = (bh + ( a + b + c)H)

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

Properties

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

It has a complete of 9 edges, 5 faces, and 6 vertices(which are joined through the rectangle-shaped faces).It has two triangle bases and three rectangle-shaped sides.If the triangular bases are equilateral and also the other faces are squares, instead of a rectangle, then the triangle prism is claimed to be semiregular.

Triangular Prism Net

If we open each face of the triangular prism, us will obtain the net. The net of this prism comprises three rectangles and also two triangles. In the below figure you have the right to see the nine distinct nets.

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Solved Examples

Example 1: find the volume that the triangle prism through base is 5 cm, elevation is 10 cm, and also 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 elevation of the prism is 4cm and also the size of the next of the it is intended triangular basic is 6cm. Then uncover the area that the prism because that the over example.

Solutions: We have,

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

As the base is an equilateral triangle, thus all its sides will certainly 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 – FAQs


What is a triangular prism?


A triangle prism is polyhedron and also a three-dimensional shape that has actually 5 faces, 6 edges and 9 vertices. Its bases space triangular and sides are rectangular.

See more: Which Colors Of Light Are Most Effective For Photosynthesis ?


How numerous faces, edges and vertices a triangular prism has?


A triangle prism has actually 5 encounters (3 rectangular and also 2 triangular), 9 vertices and also 6 edges.