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In geometry, you might have come across two solid shapes – prism and pyramid. Both prism and pyramid are three-dimensional (3D) shapes with vertices, edges, and faces. In this article, we’ll understand what is the difference between prism and pyramid.
What is a Solid Shape?
Solid shapes are solids that consist of 3 dimensions, viz. length, breadth, and height. Solid shapes are also known as 3D shapes. These solid shapes occupy space and are found in our day-to-day life.
We can touch, feel these shapes and use them in our daily life. Examples of solid shapes are spheres (ball, globe, glass marble), cylinders (juice cans, trash bin), cones, prisms, and pyramids.
What is a Prism?
A prism is a three-dimensional solid object in which the two ends are n-sided polygons and identical and lateral faces are parallelograms or rectangles.
For example, a prism with a square base is called a square prism, and a prism with a base of a pentagon is called a pentagonal prism.
Cross Section of a Prism
The cross-section is the shape obtained by the intersection of an object by a plane along its axis. If a prism is intersected by a plane, parallel to the base, then the shape of the cross-section will be the same as the base. For example, if a square pyramid is cut by a plane, parallel to the base, then the shape of the cross-section of the prism will also be a square.
Lateral Faces of a Prism
The faces joining the two bases of a prism are called lateral faces of a prism. For a right prism, the lateral faces are rectangles and in the case of an oblique prism, the lateral faces are parallelograms.
Types of Prism
Depending on the cross-section of the prism, it can be classified as
- Regular Prism: If the bases of the prism are in the shape of a regular polygon, it is called a regular prism.
- Irregular Prism: If the bases are in the shape of an irregular polygon, then the prism is called an irregular prism.
Depending on the shape of a base (number of sides of a base), a prism can be classified as
- Triangular prism (with triangular bases)
- Square prism (with square bases)
- Rectangular prism (with rectangular bases)
- Pentagonal prism (with pentagonal bases)
- Hexagonal prism (with hexagonal bases)
Depending on the shape of the lateral faces, a prism can be classified as
- Right Prism: In the right prism faces and the joining edges are perpendicular to the base faces hence the lateral faces are rectangles.
- Oblique Prism: In the oblique prism faces and the joining edges are not perpendicular to the base faces hence the lateral faces are parallelograms.
Vertices, Edges, and Faces of a Prism
For a prism with $n$-sided bases
- Number of vertices = $2n$
- Number of edges = $3n$
- Number of faces = $n + 2$
For example, for a triangular prism, $n = 3$
- Number of vertices = 6
- Number of edges = 9
- Number of faces = 5
For a pentagonal prism, $n = 5$,
- Number of vertices = 10
- Number of edges = 15
- Number of faces = 7
Surface Area and Volume of a Prism
Surface Area of a Prism: The surface area of the prism is the total area covered by the faces of the prism.
Surface Area of a Prism = 2(Base Area) + (Base perimeter × height)
Volume of a Prism: The volume of the prism is defined as the product of the base area and the prism height.
Volume of Prism = Base Area × Height
What is a Pyramid?
A pyramid is a three-dimensional shape consisting of a polygonal base and flat triangular faces (known as lateral faces) which join at a common point called the apex. For example, a pyramid with a square base is called a square pyramid, and a pyramid with a base a pentagon is called a pentagonal pyramid.
Cross Section of a Pyramid
The cross-section of a pyramid that is perpendicular to the base is a triangle and the cross-section of a pyramid that is parallel to the base is a smaller version of the base.
Lateral Faces of a Pyramid
The faces joining the apex and the base of a pyramid are called lateral faces of a pyramid. For a pyramid the lateral faces are triangles.
Types of Pyramid
Depending on the cross-section of the pyramid, it can be classified as
- Regular Pyramid: If the base of the pyramid is in the shape of a regular polygon, it is called a regular pyramid.
- Irregular Pyramid: If the base is in the shape of an irregular polygon, then the pyramid is called an irregular pyramid.
Depending on the shape of a base (number of sides of a base), a prism can be classified as
- Triangular pyramid (with triangular base)
- Square pyramid (with square base)
- Rectangular pyramid (with rectangular base)
- Pentagonal pyramid (with pentagonal base)
- Hexagonal pyramid (with hexagonal base)
Depending on the shape of the lateral faces, a pyramid can be classified as
- Right Pyramid: The apex of the pyramid is exactly over the middle of the base, hence named the right pyramid.
- Oblique Pyramid: The apex of the pyramid is not exactly over the middle of its base and is named an oblique pyramid.
Vertices, Edges, and Faces of a Pyramid
For a pyramid with $n$-sided bases
- Number of vertices = $n + 1$
- Number of edges = $2n$
- Number of faces = $n + 1$
For example, for a triangular pyramid, $n$ = 3
- Number of vertices = 4
- Number of edges = 6
- Number of faces = 4
For a pentagonal pyramid, $n$ = 5,
- Number of vertices = 6
- Number of edges = 10
- Number of faces = 6
Surface Area and Volume of a Pyramid
Surface Area of a Pyramid: Total Surface Area of Pyramid = $ \frac {1}{2} P \times l + B $ square units
where,
$P$ is the perimeter of the base
$l$ is the slant height
$B$ is the base area.
Volume of a Pyramid: The general form to find the volume of the pyramid is one-third of the base area and the height of the pyramid, i.e.,
The volume of the pyramid = $\frac {1}{3} \times $ (Base Area)$\times $(Height) Cubic units
Similarities Between Prism and Pyramid
Following are the similarities between a prism and a pyramid.
- Both prism and pyramid have 3-dimensional shapes.
- All the sides of the prism and pyramid meet at the bases.
- Both pyramids and prisms do have not round sides.
- Both are solid Geometrical shapes.
- Both have flat bases.
Difference Between Prism and Pyramid
Following is the difference between prism and pyramid.
| Parameter | Prism | Pyramid |
| Shape | A prism has two identical ends and all flat sides. | A pyramid has a base, and all sides lead from the base to join at the top point. |
| Number of Bases | Two Bases. The bases are joined together by the sides. | One Base |
| Sides (Lateral Faces) | The sides or faces are perpendicular to the base faces, i.e. they make a right angle with the base. In case the sides are not perpendicular to the base it is called an oblique prism. | The sides are triangular in shape that meets at a point on the top called an apex. |
| Apex | Does not have an apex | Has an apex |
Practice Questions
- What is a prism?
- What is a pyramid?
- How many edges, vertices, and faces are there in the prism?
- How many edges, vertices, and faces are there in the pyramid?
- What is the difference between prism and pyramid?
FAQs
What is a prism?
A prism is a three-dimensional solid object in which the two ends are n-sided polygons and identical and lateral faces are parallelograms or rectangles.
What is a pyramid?
A pyramid is a three-dimensional shape consisting of a polygonal base and flat triangular faces (known as lateral faces) which join at a common point called the apex.
What are the similarities between a prism and a pyramid?
These are the similarities between prism and pyramid:
a) Both prism and pyramid have 3-dimensional shapes.
b) All the sides of the prism and pyramid meet at the bases.
c) Both pyramids and prisms do have not round sides.
d) Both are solid Geometrical shapes.
e) Both have flat bases.
Conclusion
Prisms and pyramids are solid geometric shapes that have flat sides, flat bases, and angles. However, the bases and side faces of prisms and pyramids differ. Prisms have two bases, whereas pyramids only have one.
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