The main Difference between Pyramid and Prism is a pyramid has a single polygonal base, and its lateral faces are triangles that converge at a single point called the apex. Essentially, it has only one base and one apex, whereas a prism has two congruent polygonal bases that are parallel to each other, and its lateral faces are parallelograms that connect the corresponding vertices of the bases. In essence, it has two bases aligned in the same plane.
Table of Contents
What is 3D figure?
3D shapes are solid shapes or figures that have three dimensions, length, breadth, and height. Examples include cube, sphere, pyramid, prism, cone, and cylinder etc.
Pyramid Definition
A pyramid is a geometric solid with a polygonal base and triangular faces that meet at a common vertex. The base can be any polygon, but the most common are square-based-pyramids (with a square base) and triangular-based-pyramids (with a triangular base).
Pyramids are classified based on the shape of their base and the arrangement of their faces. For example, a square pyramid has a square base and four triangular faces, while a triangular pyramid has a triangular base and three triangular faces.
Pyramids are often studied in geometry due to their simplicity and prevalence in architecture and nature. They have various properties and formulas used to calculate their surface area, volume and other geometric characteristics.
Examples of Pyramid: The Egyptian Pyramids, the pyramids of Giza, Cone, and Tetrahedron etc.
Cross Section of a Pyramid
The cross-section of a pyramid is the shape formed by slicing through the pyramid with a plane perpendicular to its base, resulting in a polygonal shape.
Types of Pyramid
- Regular pyramid- A regular pyramid is a pyramid whose base is a regular polygon and whose lateral edges are all equal in length, and its lateral faces are congruent isosceles triangles.
- Irregular pyramid- A irregular pyramid is a pyramid whose base is not a regular polygon, and its lateral faces are not congruent isosceles triangles.
Application of Pyramids
Pyramids are used in architecture, mathematics, optics, education, and entertainment etc.
Surface Area and Volume of a Pyramid
- Lateral Surface Area of a Pyramid- ½× Perimeter of Base × Slant height
- Total Surface Area of a Pyramid- Lateral surface area + Area of base
- Volume of a Pyramid- 1/3 × Area of base × Height
Prism Definition
A prism is a three-dimensional geometric shape characterized by two congruent, parallel bases that are polygons and flat rectangular or parallelogram-shaped sides. These sides connect corresponding vertices of the bases, forming a serious of parallelograms. Prism are named based on the shape of their bases; common examples include rectangular prisms, triangular prisms, and hexagonal prisms.
The key feature of a prism is that its cross-section, taken perpendicular to its bases, remains the same along its entire length. This property distinguishes prisms from other three-dimensional shapes.
Examples of Prism: Cube, Rectangular prism, Pentagonal prism, and certain types of containers like cereal boxes etc.
Cross Section of a Prism
A cross-section of a prism is the shape you would see if you were to slice the prism perpendicular to its base.
Types of Prism
- Regular Prism- A prism whose base is a regular polygon is called regular prism.
- Irregular Prism- A prism whose is a irregular polygon is called irregular prism.
Application of Prisms
Prisms are used in optics, architecture, education, art, and also applied in physics, and photography etc.
Surface Area and Volume of a Prism
- Lateral Surface Area of a Prism- Perimeter of Base × Height
- Total Surface Area of a Prism- Lateral Surface Area + Area of 2 Bases.
- Volume of a Prism- Area of Base × Height
Key Differences:
- Number of Bases: Pyramids have one polygonal base, while prisms have two congruent polygonal bases.
- Shape of Lateral Faces: In pyramids, the lateral faces are triangular, whereas in prisms, they have parallelograms.
- Edges: Pyramids have one apex where all lateral faces meet, while prisms have lateral edges connecting corresponding vertices of the bases.
- Volume Formula: The formula for the volume of a pyramid is [(1/3) × base area × height], while for a prism, it’s [Base area × Height].
- Examples: Examples of pyramid include the Egyptian pyramids or a tetrahedron (a pyramid with a triangular base), while examples of prisms include rectangular prisms (like boxes) or triangular prisms.
Difference between Pyramid and Prism
| Pyramid | Prism |
| 1. A pyramid is a polyhedron with a polygonal base and triangular faces that meet at a common vertex. | 1. A prism is a polyhedron with two parallel polygonal bases connected by parallelogram faces. |
| 2. Pyramids have a single apex or vertex. | 2. Prisms have two identical bases and their faces are parallelograms. |
| 3. The number of triangular faces in a pyramid is determined by the number of sides in its base polygon. | 3. The number of faces in a prism depends on the number of sides in its base polygon. |
| 4. The height of a pyramid is the perpendicular distance from the base to the apex. | 4. The height of a prism is the perpendicular distance between the two bases. |
| 5. The volume of a pyramid is calculated using the formula: V = [1/3 × Base area × Height]. | 5. The volume of a prism is calculated using the formula: V= [Base area × Height]. |
| 6. Pyramids are named based on the shape of their base polygon, such as square pyramid, triangular pyramid etc. | 6. Prisms are named based on the shape of their base polygon, such as rectangular prism, triangular prism etc. |
| 7. Examples of pyramids include The Egyptian pyramids, cone, and tetrahedron. | 7. Examples of prisms include rectangular prism, cube, triangular prism, and pentagonal prism. |
| 8. Pyramids are often used in architecture, such as in the design of buildings, monuments, and roofs. | 8. Prisms are commonly found in everyday objects like boxes, buildings and certain crystals. |
| 9. Pyramids have slanting faces meeting at a vertex, giving them a pointed or tapered appearance. | 9. Prisms have flat faces that are parallel to each other, giving them a uniform cross-section throughout their height. |
| 10. The lateral faces of a pyramid are triangles. | 10. The lateral faces of a prism are parallelograms. |
Similarities between Pyramid and Prism
- Pyramid and Prism are important shapes in geometry and have many practical applications in architecture, engineering, and other fields.
- Pyramid and Prism both are solid figures with three dimension (Length, Breadth, and Height).
- Pyramid and Prism both have polygons for bases and are considered polyhedron.
- They both have edges, which are the line segments where faces meet.
- Pyramid and Prism both have vertices, which are the points where edges meet.
Practice Questions
- What is Pyramid?
- What is Prism?
- What are the difference between pyramid and prism?
- How many edges, vertices, and faces are there in the pyramid?
Recommended Reading
Basic Trigonometry Formulas for Beginners in 2024- Definition, Table, all Important Formulas & FAQs.
Area of Triangle Class 9- Definition, Important Formulas, Examples, Practice Questions & FAQs.
FAQs
Q.1 What are the difference between Pyramid and Prism?
Answer- The main difference between Pyramid and Prism is pyramids have one polygonal base, while prisms have two congruent polygonal bases.
Q.2 What are the similarities between Pyramid and Prism?
Answer- Pyramid and Prism are solid figures with 3-dimension, and both are important shapes in geometry.
Q.3 Is a pyramid half of a Prism?
Answer- The volume of a pyramid is one third of the volume of a prism.
Q.4 What is Pyramid?
Answer- A pyramid is a polyhedron with a polygon base and triangular faces that meet at a common point called the apex.
Q.5 What is Prism?
Answer- A prism is a polyhedron with two parallel congruent faces called bases and rectangular and parallelogram lateral faces.
Q.6 What are some examples of pyramids in real life?
Answer- The Egyptian pyramids, the pyramids of Giza, and the roofs of some buildings.
Q.7 What are some examples of prism in real life?
Answer- Rectangular boxes, buildings with rectangular and square bases, and certain types of containers like cereal boxes.