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

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Triangular Prism is a pentahedron and has nine distinctive nets. The edges and vertices the the bases are joined through each various other via three rectangle-shaped sides.


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

The political parties of triangle prism, which are rectangular in form are joint with each other side by side. Every cross-sections parallel to the base faces are the same as a triangle. A triangular pyramid has four triangular bases unequal the triangle prism, joined with each other and all space congruent to each other.


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Definition

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

The sides and bases of the triangular prism space congruent or else oblique. The edges of the prism sign up with the matching sides. The two bases of this prism space equilateral triangles and also edges of this triangles space parallel to every other. View the listed below figure to recognize the structure.

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Other species of Prisms

Right triangular Prism

A right triangular prism has its three rectangular sides congruent. Also, the two triangular bases space parallel and congruent to every other. The rectangular or lateral faces are perpendicular come the triangle bases.

Volume

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


Volume = Area that 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 base length, h is the elevation of the triangle and also l is the length between the triangular bases.

Surface Area

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


Surface area of triangular prism = 2A + PH

Where, 

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

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

If a, b and also c room the political parties of the triangle bases, then,

Perimeter that the base = a + b + c

Therefore,

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


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

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

Properties

Let us talk about some that the properties of the triangle prism.

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

Triangular Prism Net

If we open each face of the triangle prism, we will gain the net. The network of this prism comprises 3 rectangles and two triangles. In the listed below figure you deserve to see the nine distinctive nets.

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Solved Examples

Example 1: uncover the volume the the triangle prism through base is 5 cm, height is 10 cm, and 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 the size of the side of the equilateral triangular base is 6cm. Then uncover the area of 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, therefore all its 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 triangular prism?


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

See more: Can Sperm Leak Out The Base Of A Condom Even If It Doesn'T Break?


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


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