Real-Life Applications of Pyramid Shapes in Maths
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: Types, Properties, and Formulas
1. What is a pyramid in geometry?
In geometry, a pyramid is a three-dimensional shape, or a polyhedron, formed by connecting a polygonal base to a single point called the apex. The base can be any polygon (like a triangle, square, or pentagon), and its other faces are triangles, known as lateral faces, which meet at the apex.
2. What are the main parts of a pyramid shape?
A pyramid has several distinct parts that define its structure. The primary components are:
- Base: The single polygonal face on which the pyramid rests. The shape of the base gives the pyramid its name (e.g., a square pyramid has a square base).
- Apex: The single point or corner at the top of the pyramid where all the triangular side faces meet.
- Lateral Faces: The triangular faces that connect the edges of the base to the apex.
- Edges: The straight lines where two faces meet. A pyramid has base edges and lateral edges.
- Vertices: The corners of the pyramid, including the apex and all the corners of the base.
3. How are different types of pyramids named and classified?
Pyramids are primarily classified and named based on the shape of their base. For example:
- A pyramid with a triangular base is a triangular pyramid.
- A pyramid with a square base is a square pyramid.
- A pyramid with a pentagonal base is a pentagonal pyramid.
4. How can you determine the number of faces, vertices, and edges for any pyramid?
There is a simple formula to find the number of faces, vertices, and edges of a pyramid based on the number of sides of its base. If the base polygon has 'n' sides:
- Number of Faces = n + 1 (n triangular faces + 1 base)
- Number of Vertices = n + 1 (n vertices on the base + 1 apex)
- Number of Edges = 2n (n edges on the base + n edges connecting the base to the apex)
5. What is the key difference between a pyramid and a prism?
The key difference between a pyramid and a prism lies in their bases and lateral faces. A pyramid has only one base and its lateral faces are triangles that meet at a single apex. In contrast, a prism has two identical, parallel bases, and its lateral faces are parallelograms (often rectangles) that connect the corresponding edges of the two bases.
6. Are all the triangular faces of a pyramid always identical?
No, the triangular faces of a pyramid are not always identical. They are only guaranteed to be identical (congruent) if the pyramid is a 'right pyramid' and its base is a 'regular polygon' (a polygon with all sides and angles equal). If the pyramid is oblique (tilted) or if its base is an irregular polygon, the triangular faces will have different sizes and shapes.
7. What are some real-world examples of the pyramid shape?
The most famous real-world examples are the Great Pyramids of Giza in Egypt, which have square bases. Other examples include:
- The Louvre Pyramid in Paris, a glass and metal structure.
- The shape of some rooftops and spires in architecture.
- Certain types of tents or teepees.
- A tetrahedron-shaped tea bag, which is a triangular pyramid.
8. How is a pyramid different from a cone?
The primary difference between a pyramid and a cone is the shape of their base. A pyramid always has a polygonal base with flat sides (e.g., a square or triangle), which results in flat, triangular lateral faces. A cone, on the other hand, has a circular base and a single, curved lateral surface that tapers to an apex.
