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

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


Facts:Number of faces = 5Number of edge = 9Number the vertices = 6Shape the the basic = TriangularShape of sides = RectangularSurface Area = 2(Area of triangular bases)+Perimeter of base x height of prismVolume = Area of base x height of Prism

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


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Definition

In geometry, a triangular prism is a kind of prism with 3 sides and two bases. The sides space of rectangle shape and also bases room of triangle shape. Altogether, that has 5 faces, nine vertices and six edges. 

The sides and bases of the triangular prism are congruent or else oblique. The edge of the prism join the equivalent sides. The two bases that this prism room equilateral triangles and also edges of this triangles space parallel to every other. Watch the listed below figure to know the structure.

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Other species of Prisms

Right triangular Prism

A best triangular prism has its three rectangle-shaped sides congruent. Also, the two triangular bases space parallel and congruent to each other. The rectangular or lateral encounters are perpendicular to the triangle bases.

Volume

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


Volume = Area the the basic × elevation 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 base 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 equal to the sum of the lateral surface ar area and also twice the basic area the the triangle prism. It is measure up in square units.


Surface area of triangle prism = 2A + PH

Where, 

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

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

If a, b and c room the sides of the triangle 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 that the triangle Prism = (bh + ( a + b + c)H)

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

Properties

Let us discuss some that the properties of the triangular prism.

It has a full of 9 edges, 5 faces, and 6 vertices(which space joined through the rectangle-shaped faces).It has two triangular bases and three rectangle-shaped sides.If the triangular bases room equilateral and the other deals with are squares, instead of a rectangle, then the triangular prism is said to it is in semiregular.

Triangular Prism Net

If we open up each face of the triangle prism, we will get the net. The network of this prism comprises 3 rectangles and two triangles. In the listed below figure you have the right to see the nine distinct nets.

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Solved Examples

Example 1: discover the volume of the triangular 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 height of the prism is 4cm and also the size of the next of the it is intended triangular basic is 6cm. Then discover the area that 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 it is provided triangle, as such all that sides will certainly be equal.

Hence, a = b = c = 6cm.

By the formula,

Area the the triangle 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 form that has actually 5 faces, 6 edges and also 9 vertices. That bases are triangular and sides space rectangular.

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How countless faces, edges and also vertices a triangle prism has?


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