People often get confused between prism and pyramid due to their very similar appearance. But there are plenty of differences that distinguish them into two geometrical categories.

The prism, on one hand, has two bases that are congruent to each other. Its sides are rectangular in shape. As well as these sides are perpendicular to both the bases.

In contrast, the pyramid is a structure with only one polygonal base. Its sides are triangular in shape. These sides meet at the common meeting point, i.e., vertex.

There is no apex or apical point in prisms. Whereas the apical end or the apex are typically found in pyramids.

The prism is generally made up of glass or crystal. Thus, it manifests the phenomena like refraction or rainbow spectrum of light. For this reason, it deals with geometry as well as optics.

In contrast, the pyramids are made of a variety of substances and not just only of glass. Thus, it may or may not exhibit the split of light in a rainbow spectrum.

In the following section, we will briefly learn key differences between prisms and pyramids.

## Content: Prism Vs Pyramid

### Comparison Chart

Basis of Comparison | Prism | Pyramid |
---|---|---|

Definition | A prism is a 3-D polyhedron shaped structure having a pair of polygonal bases with rectangular sides that are perpendicular to the bases. | A pyramid is also a 3-D polyhedron structure with a polygonal base and triangular sides. |

Structure | The structure of a prism constitutes two polygonal bases of the exact same size and shape. | The structure of the pyramid constitutes one single polygon, and the triangular sides meet at a common point called vertex. |

Description | It is like pieces of glass, plastic or crystal that are capable of bending the beam of light, causing it to split in the rainbow spectrum. | A pyramid is made from various substances; thus, it may or may not show the light spectrum. |

Examples | • Pentagonal prism • Hexagonal prism • Triangular prism • Octagonal prism | • Pentagonal pyramid • Hexagonal pyramid • Triangular pyramid • Octagonal pyramid |

Shape of Slides | The prisms have rectangular-shaped sides that are perpendicular to the base. | The pyramids consist of triangular sides that join at the apex. |

Top and Bottom Surface | The top and bottom surfaces are congruent. | It has no separated top or bottom; instead, there is only one base with a pointed top. |

Number of Bases | Has 2 congruent bases. | Has only one base. |

Shape of Bases | There are two polygonal bases of prism. | There is only a single polygonal base in the case of pyramids. |

Presence of an Apex | They don't possess any apex. | They have one apex at which all the is sides meet. |

Ends | It consists of 2 opposite ends that have a parallel arrangement to each other. | There is one polygonal base is flat. |

Subject related | It is utilized in the fields like optics and geometry. | They are only used geometrical field only. |

### What is a Prism?

You can imagine the prisms just like cylinders with pointed edges and a polygonal shape at the bases. The prisms fall under the subclass prismatoid.

We can define a prism as “* A prism is a polyhedron structure having an exact number of faces equivalent to that of sides of its polygonal base*.”.

For more easy understanding, you can remember the three basic properties of prism:

- Identical ends/bases
- Parallel ends/bases
- Flat surfaces

Prisms are named according to their respective bases. For example, a prism with a triangular base will be a triangular prism.

#### Examples of Prism

#### Characteristics of Prism

- It is a 3-dimensional polyhedron.
- Their sides are rectangular and meet with two adjacent sides at the edge.
- The sides are at a 90-degree angle from the base, i.e., the sides are perpendicular to their respective bases.

**Note: However, the sides are not perpendicular to the base in some prisms. We refer to such prisms as oblique prisms.**

- The prisms do not have an apical point or apex where all the sides meet.
- They comprise two bases or two ends.
- The bases of the prism are identical and exactly parallel to each other.
- The base region is always flat.

#### Drawing a Prism

Inflate any 2-D polygonal shape to make it 3-D. For example, to draw a triangular prism, make a triangle base. Duplicate the triangle a few inches away in a parallel manner. Further, join the points of the original triangle to the corresponding points of a duplicated triangle with the help of a ruler. You can highlight the bases by colouring or shading.

#### Surface Area of Prism

You can calculate the surface area of the prism by adding twice the area of the base to the product of the base perimeter and height.

**S.A. (Prism) = [ 2 x Area of base] + [ Perimeter of base x Height]**

#### Volume of Prism

You can calculate the volume of the prism by multiplying the area of parallel bases by the height of the prism.

**Volume (Prism) = Area of base x Height of prism**

#### Uses of Prism

As the prisms are generally of glasses or crystals, thus their surface is highly sharp and polished. For this reason, they manifest the phenomenons like refraction and reflection. And the phenomenon of splitting the white light into its constituent seven rainbow colours.

Thus, prism is helpful in studies related to optics and geometry.

### What is a Pyramid?

You can understand a pyramid just like a cone with a specified polygonal shape at the bottom. They are basically polyhedra consisting of a polygonal base with a triangle on each side.

You might have heard about the “**Pyramid of Giza**” in Egypt and Paris’s “**Pyramide du Louvre**“. People think of pyramids just as these monuments, but instead, the pyramids are all around you. Towers, tents, temples, toys etc., are often pyramid-shaped.

There are two major criteria for any structure to be a pyramid:

- It should have one polygonal base.
- All the faces attached to the base should be triangular.

There are different types of pyramids on the basis of the respective shapes of their base. For instance, a pyramid with a pentagonal base is a pentagonal pyramid.

#### Examples of Prism

#### Characteristics of Pyramids

- It is a 3-D structure.
- They possess a single polygonal base.
- They consist of an apex point at the very centre of the pyramid. All the sides of a pyramid meet at this point.
- They bear triangular faces.
- Similar to the prisms, the pyramids also get their name based on the shape of the base.
- The faces of the pyramid are inclined towards the inner side at a certain angle. These faces meet at a common point, i.e., apex.

#### Drawing a Pyramid

You can simply draw a pyramid by taking any polygonal base and joining the vertices of the base to the apex.

For instance, draw a slanted parallelogram as a base to make a basic right pyramid. Point a small dot parallel to the centre of the base. Now with the help of the ruler join all the vertices of the base to the apex point taken above. You can mark or shade the base to make it more distinct.

#### Surface Area of the Pyramid

**Lateral Surface Area of the Pyramid**

You can calculate the lateral surface area of the pyramid by taking half of the product of the pyramid’s perimeter and the height of the pyramid.

**L.S.A. (Pyramid) = ½ [Perimeter of prism x height]**

**Total Surface Area of the Pyramid**

This can be calculated taking half the sum of the products of perimeter and height and the area of the pyramid’s base.

**T.S.A. (Pyramid) = ½ [ (Perimeter of prism x height) + Area of base]**

#### Volume of the Pyramid

You can calculate the volume of a pyramid by multiplying 1/3 to the product of the area of the base and the height of the pyramid.

**Volume (Pyramid) = 1/3 x (Perimeter of prism x height)**

#### Uses of Pyramid

The pyramids are vital structures in the fields like geometry. These pyramids form the shape of some elementary things around. Thus, knowing about them in detail helps to assert our surrounding shapes.

## Key Differences Between Prism and Pyramid

- The prism on one side has two identical and parallel bases. Whereas the pyramid only consists of a single base.
- The faces or sides of the prism are always rectangular or a parallelogram. But that of pyramids are triangular in shape.
- Prisms do not possess an apex point. In contrast, the pyramids consist of the apex point that acts as a point of junction for the meeting of all the sides.
- The sides of a prism are perpendicular to its base. But, in pyramids, these sides are inclined at a certain angle.
- The prism is related to both geometries as well as optics. Whereas the pyramids

### Conclusion

Both prism and pyramid are polyhedrons but they greatly vary in their structures. They are present everywhere around. This post will help you understand the basic criteria to distinguish between this nearly same structure which might often confuse you.

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