A triangular prism is a polyhedron, (three-dimensional shape) made up of two triangular bases and 3 rectangular sides. Like other Prisms, the 2 bases right here are parallel and also congruent to each various other. It has actually 5 faces, 6 vertices and 9 edges in full.

You are watching: How many vertices does a triangular prism have Triangular Prism is a pentahedron and also has actually nine distinctive nets. The edges and also vertices of the bases are joined through each various other via 3 rectangular sides.

 Facts:Number of deals with = 5Number of edges = 9Number of vertices = 6Shape of the base = TriangularShape of Sides = RectangularSurconfront Area = 2(Area of triangular bases)+Perimeter of base x Height of prismVolume = Area of base x Height of Prism

The sides of triangular prism, which are rectangular in shape are joint with each various other side by side. All cross-sections parallel to the base faces are the same as a triangle. A triangular pyramid has actually four triangular bases unlike the triangular prism, joined through each various other and also all are congruent to each various other.

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## Definition

In geomeattempt, a triangular prism is a form of prism with 3 sides and 2 bases. The sides are of rectangle form and also bases are of triangle form. Altogether, it has 5 encounters, nine vertices and six edges.

The sides and bases of the triangular prism are congruent or else oblique. The edges of the prism join the equivalent sides. The two bases of this prism are equilateral triangles and edges of these triangles are parallel to each various other. See the below number to understand the structure. ## Right Triangular Prism

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

## Volume

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

 Volume = Area of the Base × Height of prism

Due to the fact that, 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 elevation of the triangle and also l is the size in between the triangular bases.

## Surface Area

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

 Surface area of triangular prism = 2A + PH

Wbelow,

A is the location 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

Thus,

Surchallenge location 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 also h is the base and also elevation of the bases, respectively and also H is the height of the prism.

## Properties

Let us talk about some of the properties of the triangular prism.

It has a full of 9 edges, 5 deals with, and 6 vertices(which are joined by the rectangular faces).It has actually 2 triangular bases and three rectangular sides.If the triangular bases are equilateral and also the various other encounters are squares, rather of a rectangle, then the triangular prism is said to be semiconsistent.

## 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 also two triangles. In the listed below number you have the right to see the nine distinctive nets. ## Solved Examples

Example 1: Find the volume of the triangular prism through base is 5 cm, height 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 length of the side of the equilateral triangular base is 6cm. Then uncover the area of the prism for the over example.

Solutions: We have,

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

As the base is an equilateral triangle, therefore 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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A triangular prism is polyhedron and a three-dimensional shape that has actually 5 faces, 6 edges and 9 vertices. Its bases are triangular and sides are rectangular.