What is a Pyramid?
In Geometry, a pyramid is a polyhedron formed by joining a polygonal base and a point, known as apex or vertex. Each base edge and apex forms a triangle known as the lateral faces. It is a three-dimensional geometric shape with a polygon base. A pyramid with an ‘x’ sided base has (x +1 ) vertices, (x + 1 ) faces, and (2x) edges. A pyramid is generally described by the shape of its base. For example, a triangular pyramid has a triangular base whereas a hexagonal pyramid has a hexagonal base.
Pyramid Image
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Parts of 3D Triangle Shape- Pyramid
Apex
An apex is the vertex of a pyramid at its top.
Edge
The line segments formed by joining two intersecting faces are the edges of a pyramid.
Lateral Face
The lateral faces of a pyramid shape are congruent isosceles triangles.
Base
A base is the bottom of the pyramid shape.
Real-Life Examples of Pyramid
Following are some of the real-life examples of pyramid
Pyramid Toy
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Pyramid Pastry
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Pyramid of Egypt
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Pyramid Chocolate
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Volume And Surface Area of Pyramid
The formula of volume of a pyramid shape is given as:
Volume = 1/3 \[\times \] Base Area \[\times \] Height |
Surface Area of Pyramid
The two parts of a surface area of the pyramid are:
Base Area ( Area of the base)
Lateral Area (Area of the side face)
When all the side faces of a pyramid shape are the same.
½ \[\times \] Base Area \[\times \] Perimetre \[\times \] Slant Height |
When all the side faces of a pyramid are different.
Base Area + Lateral Area |
Types of Pyramid
Following are the different types of the pyramid:
Square - Based Pyramid
A square-based pyramid is a three-dimensional object with a square base. It has four triangular faces/sides, 5 vertices, and 8 edges. The Egyptian pyramid is the best example of a square-based pyramid.
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A square-based pyramid is also known as a pentahedron because it has a total 5 faces- Penta means 5 in Latin. Out of 5 faces, 4 faces are triangular in shape and 1 face ( the polygon on which it rests upon) is square in shape.
If all the four triangles of a square-based pyramid are equilateral with equal sides and angles, then the square -based pyramid is referred to as Johnson Solid.
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Triangular Based Pyramid
A triangular-based pyramid is a solid object formed by joining a triangular base to a point known as apex or vertex. This creates 4 faces/sides, each of which is triangular in shape. It has 4 vertices and 6 edges.
A triangular based pyramid is also known as ‘Tetrahedron’ because the four faces of a triangular pyramid are triangular in shape.
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Pentagonal Pyramid
In Geometry, a pentagonal pyramid is a pyramid with a pentagonal base upon which five triangular faces are erected that meet at a point known as the apex or vertex.
The regular pentagonal pyramid is a pyramid with a base that is a regular pentagon. Also, this pyramid has 5 lateral faces that are equilateral triangles. A pentagonal pyramid is one of Johnson's solid.
It has a total of 6 faces, six vertices and 10 edges.
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Hexagonal Pyramid
In Geometry, a hexagonal pyramid is a pyramid with a hexagonal base upon which six isosceles triangles are erected that meet at a point known as the apex/vertex. A hexagonal pyramid has 7 faces, 7 vertices, and 12 edges.
Hexagonal pyramid is also known as heptahedron because it has 7 faces.
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Right V/S Oblique Pyramid
These types of pyramids tell where the top (apex) of the pyramid is. When the apex or vertex of a pyramid is found directly above the center of its base, then it is known as a regular pyramid, else it is known as an oblique pyramid.
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Regular V/S Irregular Pyramid
These types of pyramids tell about the base of the shape. When the base of a pyramid is a regular polygon, then it is considered a regular pyramid, else it is known as an irregular pyramid.
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Pyramid Questions With Examples
Find the volume of a regular square pyramid with base side 20 cm and altitude 15 cm?
Solution:
Given
Base Side = 20 cm
Accordingly, base area will be 20 \[\times \] 20 = 400 cm2
Altitude = 15 cm
The volume of a regular square pyramid can be calculated using the following formula:
⅓ \[\times \] (Base Area) \[\times \] Height
Using the formula, we get
⅓ \[\times \] 400 \[\times \] 15
= 2000
Hence, the volume of a given regular square pyramid is 2000 cm3.
What is the area of a regular square pyramid with base side 5 in and altitude 8 in?
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Solution:
Area of Base = 5 \[\times \] 5 = 25 cm2
Area of Lateral Surface = ½ \[\times \] 5 \[\times \] 8 = 20 cm2
Area of 4 sides faces = 20 + 20 + 20 + 20 = 80 cm2
Note: There are 4 identical lateral surface faces. Therefore we have counted lateral surface area 4 times.
The area of a regular square pyramid can be calculated using the formula
Surface Area = Area of Base + Area of Lateral Surface
By substituting the values in the above surface area of the pyramid formula, we get:
25 + 80
= 105 cm2
The surface area of a regular square pyramid is 105 cm2
Did You Know?
A pyramid is defined as a polyhedron that joins a polygon base (such as a triangle or square) to a point known as the apex or vertex using triangles.
The tetrahedron is the other name of a triangular pyramid. A tetrahedron has 4 triangular faces, with three faces meeting at each point known as the vertex.
An octahedron has 8 faces of an equilateral triangle, with four faces meeting at each point known as the vertex.
An icosahedron has 20 faces of identical equilateral triangles. An icosahedron pyramid has 12 vertices and 30 edges.
The great Pyramid that was built by Ancient Egyptians several years ago is an example of a square pyramid.
FAQs on Pyramid Shape
1. What best describes the pyramid shape in geometry?
A pyramid is a polyhedron that has a base which can be any polygon, and three or more triangular faces that meet at a point known as the apex. The triangular sides are also often known as lateral faces to differentiate themself from the base
2. How to make a pyramid in geometry?
In Geometry, a pyramid is formed by joining a polygonal base and a point, known as apex. Each base edge and apex together form a triangle known as the lateral faces of a triangle. A pyramid is a comical solid with a polygonal base.
3. What do all pyramids have in common in Geometry?
All different types of pyramids in Geometry are named according to the shape of their base, which is always a polygon ( such as square, triangle, pentagonal, hexagonal, etc). Although all the bases of a pyramid are different they have one thing in common i.e. their lateral faces are always triangular in shape.
4. How many bases does a pyramid have?
A pyramid is a polyhedron that has only one base. The other faces are congruent triangles, and they share a common point which is known as the apex or vertex. The base of the pyramid can be of any polygon. For example, the Pyramid of Egypt has a base square in shape and four triangular faces.
