A triangular prism is a polyhedron, (three-dimensional shape) comprised of two triangular bases and three rectangular sides. Like various other Prisms, the 2 bases right here are parallel and congruent to each 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 distinctive nets. The edges and also vertices that the bases room joined v each various other via three rectangle-shaped sides.


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

The sides of triangular prism, i beg your pardon are rectangle-shaped in form are joint with each various other side through side. All cross-sections parallel come the base faces are the same as a triangle. A triangular pyramid has 4 triangular bases unequal the triangle prism, joined with each other and 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 also two bases. The sides room of rectangle shape and bases room of triangle shape. Altogether, that has 5 faces, ripe vertices and six edges. 

The sides and bases the the triangular prism room congruent or rather oblique. The edge of the prism join the equivalent sides. The two bases of this prism space equilateral triangles and edges of these triangles room parallel to each other. See the listed below figure to understand the structure.

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Other types of Prisms

Right triangle Prism

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

Volume

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


Volume = Area that the base × elevation of prism

Since, the base is in triangle 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 l is the length in between the triangle bases.

Surface Area

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


Surface area of triangular prism = 2A + PH

Where, 

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

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

If a, b and also c are the political parties of the triangular 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 also h is the base and height the the bases, respectively and also H is the height of the prism.

Properties

Let us discuss some of the properties of the triangle prism.

It has actually a full of 9 edges, 5 faces, and 6 vertices(which are joined by the rectangle-shaped faces).It has two triangular bases and three rectangle-shaped sides.If the triangle bases room equilateral and the other deals with are squares, rather of a rectangle, then the triangle prism is stated to be semiregular.

Triangular Prism Net

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

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Solved Examples

Example 1: uncover the volume that the triangular prism v base is 5 cm, height 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 side of the it is intended triangular base is 6cm. Then discover the area the the prism because that the above example.

Solutions: We have,

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

As the base is an it is provided triangle, thus all that sides will 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 inquiries – FAQs


What is a triangle prism?


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

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


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