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# Prisms

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 Sub Topics A prism is a collection of 3 or more cross section objects like triangular prism is a collection of 3 cross section objects; square prism is a collection of 3 cross section objects. Now we discuss prism Geometry of all kind of prisms– Triangular prism: A prism, which is a collection of 3 cross section objects, is called as a triangular prism and triangular prism is a type of an irregular prism because edge length and angle of irregular prisms are not equal. For calculating the area and volume of triangular prism, we use following formula– Area of triangular prism = 2 * Area of base + Perimeter of base * H, Volume of triangular prism = Area of the base * height, Square prisms: Square prisms are collection of 4 cross section objects and it is a part of regular prism because edge length and angle of this type of prism are equal in nature. Square prisms are made from Solid material and all the faces of Square prisms have square shape. For calculating the area and volume of square prism, we use following formula– Area of square prism = l * l, where l = edge length, Volume of rectangular prism = l * l * l * l, Pentagonal prisms: pentagonal prisms are collection of 5 cross section objects and it is a part of irregular prisms because edge length and angle of these types of prism are not equal in nature. Pentagonal prisms are made from solid material and all the faces of pentagonal prisms have pentagonal shape. Cube prisms: cube prisms are collection of 6 cross section objects and it is a part of regular prisms because edge length and angle of these Types of Prisms are equal in nature. Cube prisms are made from solid material and all the faces of Cube prisms have cubical shape. This is all about prism geometry of all type of prisms.

## Base of Prism

When we collect 3 or more cross section object, then combine Solid geometry with a uniform cross section is called as a Prism like triangular prism is a collection of 3 cross section objects, square prism is a collection of 4 cross section objects. The base of a prism makes different between all type of prisms like triangular prism’s base has triangle shape, square prism’s base has Square shape and Cube prism’s base has cube shape. Now we discuss prism base of all kind of prisms:

Triangular prism: an irregular prism, whose edge length and angle are not equal and whose base has triangle shape is called as a triangular prism and for evaluating are of triangular prism, we use following formula :

Area of triangular prism = 2 * Area of base + Perimeter of base * H,
And for volume of triangular prism, we use following formula:
Volume of triangular prism = Area of the base * height,

Square prisms: A regular prism, whose base has square shape and whose edge length and angle are equal, is called as a square prism. For evaluating the area of square prism, we use following formula:

Area of square prism = length * length,
Volume of square prism, we use following formula:
Volume of rectangular prism = length * length * length * length,

Pentagonal prisms: An irregular prism, whose edge length and angle are not equal and whose base has pentagonal shape is called as a pentagonal prism.

Cube prisms: A regular prism, whose base has cube shape and whose edge length and angle are equal are called as a cube prism.

These all are type of prisms, which are differ with each other by their base of prism shape. Therefore the shape of base of a prism creates difference between Types of Prisms.

## Lateral Faces of Prism

Lateral faces are the faces which are used to join the bases of a Solid but when we calculate the lateral faces of a solid object we do not include the bases of a solid.

In this diagram we show the lateral face of Prism or an object where base is not included.

In this diagram the sides are the lateral faces and up and down side are the bases of a hexagonal prism.
Now we see how many lateral faces a pentagonal prism has.

There are five lateral faces present in a pentagonal. The lateral area of a prism = sum of all the areas of its lateral faces and the total area of a prism = sum of all the areas of all its faces. The lateral area of a Right Prism is always equal to the perimeter of a base and it is multiplied by the height of the prism.

The lateral area of a prism = p * h;
Where, ‘p’ is the perimeter of a base, and ‘h’ is the height of a prism.

And the volume of a prism is equal to the area of the base which is multiplied by the height of the prism.
Volume of a prism = b * h;

Where, ‘b’ is the base of a prism, and ‘h’ is the height of a prism. We can find out the perimeter of a prism by adding all the lateral faces of a given prism.

If we have hexagonal prism, then the perimeter of a prism is:

Perimeter = a + b + c + d + e + f;

There are some parts of prism which are:

Base – The top and bottom side of a prism.

Altitude – The line which is used to join the two bases and it is also perpendicular to both the bases.

## Lateral Edges of Prism

In mathematical Geometry, A Solid object which has two identical ends and all the other sides are flat is known as Prism.

The formula for finding the lateral area of Right Prism is given by;

The lateral area of prism= LA or,
The lateral area of prism = (p) (h),

Where ‘L’ or ‘P’ represents the perimeter of a prism, and ‘H’ represents the height of a prism,

In a prism if two bases are present and one base of a prism is directly present just above the other base of the prism is known as right prism. Now we see the formula for finding the Total area of prism. The Total area of right prism is given by:

Total area of right prism = LA + 2B or,
Total area of right prism = (p) (h) + 2B,

Where ‘L’ or ‘P’ represents the perimeter of a prism,

Now we will see the different types of prism.

Some types of prism are mention below:

1. Regular prism 2. Irregular prism
3. Right prism 4. Oblique prism
5. Parallelepipeds 6. Cuboids
7. Triangular prism 8. Square prism
9. Pentagonal Prism 10. Hexagonal prism:

Now we will see the lateral edges of prism.

Suppose we have a figure and in the figure we mention all edges, faces, length and height of a prism.

In the given figure the distance between the bases is denotes the height of a prism and lateral edges of a prism are parallel edges of equal length.

Now we will talk about the lateral area of Oblique Prism. Suppose we have an oblique prism, whose sides are 5 inch, 6 inch, 5 inch, 6 inch, 8 inch, 9 inch, and height of oblique is 12 inch, then what is the lateral area of oblique prism?

First we find the perimeter of a prism = 5 + 6 + 5 + 6 + 8 + 9;
Perimeter = 39 inch.
Height = 12 inch
LA = 39 * 12;
LA = 468 inch2,
The lateral area of an oblique prism is 468 inch2.
This is all about prism, its lateral area and total surface area.