Pyramid
In mathematics, a pyramid is a 3D figure built with a base of a polygon and triangular faces all connected together. A pyramid connects each edge of the base to a common tip or apex giving it the typical shape. Let us learn more about pyramids in this section.
Definition of Pyramid
A pyramid is a 3D polyhedron with the base of a polygon along with three or more triangleshaped faces that meet at a point above the base. The triangular sides are called faces and the point above the base is called the apex. A pyramid is made by connecting the base to the apex. Sometimes, the triangular sides are also called lateral faces to distinguish them from the base. In a pyramid, each edge of the base is connected to the apex that forms the triangular face.
Properties of a Pyramid
Here is a list of the different properties of a pyramid that help us to identify it easily:
 A pyramid is made of three main parts  apex, face, and base.
 The polygon base is most often in the shape of a square.
 The faces of the pyramid except the base are called lateral faces.
 If the base is a regular polygon, the triangles are congruent, and isosceles.
 The line segments created by two intersecting faces are called edges and the point or corner at which three or more edges meet is the vertex.
 Apex is the vertex that is opposite to the base and gives the shape to the pyramid.
Types of Pyramids
There are different types of pyramids based on the shape of their base. Let us look at the different types of pyramids:
Square Pyramid
A square pyramid is formed when the base of the pyramid is in the shape of a square. A square pyramid consists of one square base and three triangular faces. In other words, it has 8 edges, 5 vertices, and 4 faces. Observe the square pyramid shown below to understand its shape.
Triangular Pyramid
If the base of a pyramid is in the shape of a triangle, it is said to be a triangular pyramid. A triangular pyramid has 4 faces, 6 edges, and 4 vertices. This kind of pyramid can also be called a tetrahedron. Observe the triangular pyramid shown below to understand its shape.
Pentagonal Pyramid
A pentagonal pyramid is one which has its base shaped like a pentagon, with the rest of the faces as triangles. This pyramid has 6 faces, 6 vertices, and 10 edges. Observe the following pentagonal pyramid for a better understanding of its shape.
Right Pyramid vs Oblique Pyramid
The location of the apex or the top of a pyramid decides whether a pyramid is a right pyramid or an oblique pyramid. A pyramid is named as a right pyramid when the location of the apex is exactly over the middle of the base of the pyramid. Whereas, when the location of the apex is not exactly over the middle but slightly away, then that pyramid is called an oblique pyramid. In other words, when a perpendicular line from the apex intersects the centre of the base, it is a right pyramid. When it does not intersect the centre of the base, it is an oblique pyramid. Observe the following figures to see the difference between an oblique pyramid and a right pyramid.
Regular vs Irregular Pyramid
If the base of the pyramid is a regular polygon, it is considered to be a regular pyramid. If the base is an irregular polygon, where the sides are not equal to each other, then it is an irregular pyramid. Observe the following figure to notice the difference between a regular and an irregular pyramid.
Volume of a Pyramid
The volume of a pyramid refers to the space enclosed between its faces. Each pyramid has a different formula depending on the base of the pyramid. The volume of a pyramid is measured in cubic units and the formula used to calculate the volume of a pyramid is: Volume of a Pyramid = 1/3 × Base Area × Height
Surface Area of a Pyramid
The surface area of a pyramid is different for different types of pyramids. The formula used to find the surface area of a pyramid is as follows:
When all side faces are the same, the formula is: Surface Area = Base Area + (½ × Perimeter of the base × Slant height)
When side faces are different, the formula is: Surface Area = Base Area + Lateral Area
It should be noted that when the side faces are different, as in the case of irregular pyramids, we calculate the total lateral area by adding the area of each triangle.
Net of a Pyramid
The net of a pyramid is seen when the different types of pyramids are flattened and opened up. For example, the net of a square pyramid consists of a base with the shape of a square along with 4 triangle sides or faces. The net of a triangular pyramid consists of 5 faces, i.e., one square base and 4 triangular lateral faces. Observe the following figure to see the net of a pyramid.
Related Topics
Listed below are a few interesting topics related to pyramids:
Solved Examples

Example 1: Find the volume of the pyramid, if its base area is 60 unit^{2} and its height is 12 units.
Solution: Base area = 60 and height = 12
Let's calculate the volume by substituting the values in the formula.
Volume of a pyramid = 1/3 × Base Area × Height
Volume = 1/3 × 60 × 12
Volume = 240 units^{3}
Therefore, the volume of the pyramid is 240 units^{3}

Example 2: Find the surface area of a square pyramid with the given dimensions: side of the base =16 inches, slant height = 15 inches.
Solution: The perimeter of the base = 4 × 16 = 64 inches; Base area = a^{2} = 16^{2} = 256 square inches; slant height = 15 inches
Let us fill in all the dimensions in the formula:
Surface Area = Base Area + (½ × Perimeter of the base × Slant height)
Surface area = 256 + (½ × 64 × 15)
Surface area = 736 inch^{2}
Therefore, the surface area of the square pyramid is 736 inch^{2}
FAQs on Pyramid
What is a Pyramid?
A pyramid is a 3D polyhedron with the base of a polygon along with three or more triangleshaped faces that meet at a point above the base. The triangular sides and the base are called the faces and the point above the base is called the apex. One of the most famous reallife examples are the pyramids of Egypt.
What are the Different Types of Pyramids?
There are different types of pyramids that we see which are based on the shape of their bases. The various types of pyramids are as follows:
 Square pyramid  in which the base of the pyramid is a square.
 Triangular pyramid  in which the base of the pyramid is a triangle.
 Pentagonal pyramid  in which the base of the pyramid is a pentagon.
 Right pyramid  in which the apex is exactly above the middle of the base.
 Oblique pyramid  in which the apex is not exactly above the center of the base.
 Regular pyramid  in which the base is a regular polygon.
 Irregular pyramid  in which the base of the pyramid is not a regular polygon.
What is the Formula to Find the Volume of a Regular Pyramid?
Different types of pyramids have different formulas to find out the volume. The formula to find the volume of a regular pyramid is: Volume of a Pyramid = 1/3 × Base Area × Height
What is the Formula to Find the Surface Area of a Regular Prism?
Similar to the volume, each pyramid type has a different formula. The formula for a regular pyramid is as follows:
When all side faces are the same, the formula is: Surface Area = Base Area + (½ × Perimeter of the base × Slant height)
When side faces are different, the formula is: Surface Area = Base Area + Lateral Area
What is a Tetrahedron Pyramid?
A tetrahedron pyramid which is also known as a triangular pyramid is a special kind of pyramid where all its faces including the base is a triangle. This is the only type of pyramid where any side of the face can be the base of the pyramid and any of the vertices can be its apex.
What is an 8 Sided Pyramid Called?
An 8 sided pyramid is called an octagonal pyramid where the base is an octagon and the rest of the faces are triangles. The faces or the triangular sides of the pyramid meet at a point directly above the base.