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

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


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

The sides of triangle prism, which are rectangular in shape are joint with each various other side through side. Every cross-sections parallel to the base deals with are the very same as a triangle. A triangular pyramid has four triangular bases uneven the triangular prism, joined with each other and all are congruent to every other.


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Definition

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

The sides and also bases that the triangular prism space congruent or else oblique. The edge of the prism join the matching sides. The 2 bases that this prism room equilateral triangles and edges of this triangles are parallel to every other. Check out the listed below figure to know the structure.

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Other varieties of Prisms

Right triangle Prism

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

Volume

The volume of a triangle prism is equal to the product the the triangular base area and the elevation of the prism.


Volume = Area of the basic × height of prism

Since, the basic is in triangular shape, therefore,

Area = ½ b h

Hence,


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

Where b is the basic length, h is the elevation of the triangle and l is the length between the triangular bases.

Surface Area

Surface area of triangle prism is same to the sum of the lateral surface area and twice the basic area that the triangular prism. It is measure up in square units.


Surface area of triangular prism = 2A + PH

Where, 

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

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

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

Perimeter that the base = 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 also height the the bases, respectively and also H is the elevation of the prism.

Properties

Let us comment on some the the nature of the triangle prism.

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

Triangular Prism Net

If we open up each challenge of the triangle prism, us will gain the net. The network of this prism comprises three rectangles and also two triangles. In the below figure you have the right to see the nine unique nets.

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Solved Examples

Example 1: uncover the volume the the triangular prism through base is 5 cm, elevation is 10 cm, and also length is 15 cm.

Solution: Volume of triangle 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 the length of the next of the equilateral triangular basic is 6cm. Then find the area the the prism for the above 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 the sides will certainly be equal.

Hence, a = b = c = 6cm.

By the formula,

Area the 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 inquiries – FAQs


What is a triangle prism?


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

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


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