Pyramid: Properties, Types, and Formula

A pyramid is a three-dimensional structure with a polygonal basis. You've certainly heard of The Great Pyramid of Giza, constructed along similar lines. Every corner of this structure is connected to a single apex, giving it the illusion of a one-of-a-kind shape. In geometry, a pyramid is known as a polyhedron. It comprises a base and three or more triangular faces that meet above the base (the apex). A pyramid's base, edge, and peak create a triangle known as a lateral face. A pyramid is defined as a self-dual conic solid with a polygonal base. A pyramid has n + 1 vertices, n + 1 faces, and 2n edges, as well as an n-sided base. The apex of a right pyramid is immediately above the centroid of its base. Oblique pyramids are not on the right side of the pyramid.

Key Terms: Pyramid, triangular pyramid, Pythagoras theorem, edges, surface area of a pyramid, volume of a pyramid

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Pyramid

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A pyramid is a three-dimensional polyhedron with a polygonal base and three or more triangle-shaped faces that intersect at the top. The triangle sides are referred to as faces, while the point above the base is the apex. A pyramid is built by linking the base and peak. To distinguish them from the base, the triangular sides are typically referred to as lateral faces. The triangular face is formed by connecting each edge of the pyramid's base to the summit.

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Properties of a Pyramid

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Some of the qualities of a pyramid that may assist you in identifying it are as follows:

• The opposite vertex from the base that gives the pyramid its form is the apex.
• A pyramid comprises three major components: the apex, the face, and the base.
• The triangles are congruent and isosceles if the base is a regular polygon.
• The most common polygon foundation form is square.
• The vertex is the point or corner at which three or more edges meet, whereas edges are the line segments formed by two intersecting faces.
• Except for the base, the faces of the pyramid are referred to as lateral faces.

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Types of Pyramids

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The shape of the base of a pyramid determines its classification. Let's have a look at the many forms of pyramids:

Square Pyramid

When the pyramid's base is square, a square pyramid is formed. A square pyramid has one square foundation and three triangle faces. In other words, it contains eight edges, five vertices, and four faces. Take a look at the square pyramid displayed below to understand its shape.

Square pyramid

Triangular Pyramid

If the base of a pyramid is formed like a triangle, it is triangular. A triangular pyramid has four faces, six edges, and four vertices. A tetrahedron is another name for this sort of pyramid. 

Triangular pyramid

Pentagonal Pyramid

A pentagonal pyramid has a base fashioned like a pentagon, while the other faces are triangles. This pyramid comprises six faces, six vertices, and ten edges. 

Pentagonal Pyramid

Right Pyramid vs Oblique Pyramid

The position of the apex or top of a pyramid defines whether it is a right pyramid or an oblique pyramid. A right pyramid is one in which the pyramid's pinnacle is directly above the centre of the pyramid's base. The summit of a pyramid is an oblique pyramid when it is not squarely above the centre but is somewhat away. In other words, a right pyramid is produced when a perpendicular line from the top intersects the base's centre. An oblique pyramid does not intersect the base's centre. 

Right Pyramid vs Oblique Pyramid

Regular vs Irregular Pyramid

A regular pyramid has a regular polygon as its foundation. If the base is an irregular polygon with sides that are not equal, the pyramid is irregular. 

Regular vs Irregular Pyramid

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Surface Area of a Pyramid

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The surface area of a pyramid is defined as the number of square units required to cover the whole surface of the pyramid. The total surface area may also be defined as the sum of the areas occupied by each of its surfaces.

Because all of the surfaces are identical, calculating the surface area of the proper pyramid is straightforward. Consequently, we only need to compute the area of one of the surfaces. By adding the base area, we can determine the total surface area.

Total Surface Area

Pyramid math may be used to compute the total surface area of a Pyramid as follows:

4bh² + b² = area

In this situation, b is the length of the base's side, and h is the height of the slant.

The following equation can be simplified as well:

area = b² + 2bh

• The surface area of a regular polygon is simple to calculate. Still, the area of an irregular pyramid is more complex to compute because the triangular faces of an irregular pyramid vary in form and size. The following are several ways of determining the area of an irregular pyramid.
• Triangles may be formed from pyramids. The surface areas of these triangles may be calculated individually and added. 
• A pyramid can also be represented as a regular hexagon with one triangular component removed. If we know how to calculate the surface area of the missing triangle, we can find the area of a regular hexagon and subtract the area of the missing triangle from it.
• A pyramid may be broken down into two parallelograms. Thus, the total surface area may be calculated by adding the areas of two parallelograms. 
• If the coordinates and vertices of the pyramid are known, we may calculate the area manually or with a computer programme.

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Volume of a Pyramid

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The volume of a pyramid may be defined as the number of cubic units that can fill a pyramid.

A pyramid's volume may be computed as one-third of its base area multiplied by its perpendicular height. The formula for calculating the volume of the pyramid is as follows:

volume = (1/3) x b x h

Here,

b = area of the base of the pyramid

h = height (the vertical distance between apex and base of a pyramid).

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Net of a Pyramid

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When different pyramids are flattened and opened up, the net of a pyramid is seen. The net of a square pyramid, for example, is made up of a square base and four triangular sides or faces. A triangular pyramid's net has five faces: one square base and four triangular lateral faces. 

Net of a Pyramid

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Applications of pyramids

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The applications of pyramids are:

• The Great Giza Pyramid in Egypt was built. The burial chamber of Pharaoh is located deep beneath the Pyramids.
• Traffic officers are increasingly using Pyramid construction cones to reduce the number of accidents on the road.
• Pyramids are used to accelerate the healing process.
• Egypt's largest pyramid can store electric and magnetic energy within its chambers, allowing it to generate higher quantities of energy.
• Pyramids help to reduce stress and tension in the physical body.
• A pyramid can help to restore energy flow in the human body.
• Pyramids offer high-energy spaces that are suitable for meditation.
• A Pyramid strengthens the power of purpose while also harmonising the environment.

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Things to remember

• A pyramid is a three-dimensional geometric shape with a polygonal base and triangular lateral surfaces that meet at a common vertex.
• Although the four-sided pyramid with base is the most common variant, a pyramid must have at least three outside triangular surfaces plus the base.
• The Surface Area is split into two parts: the base area (the Base Area) and the area of the side faces (the Area of the Side Faces) (the Lateral Area). 
• When the side faces of a pyramid differ (as in an "irregular" pyramid), we must sum the area of each triangle to calculate the overall lateral area.
• The Triangular Pyramid is a Tetrahedron with four faces, three of which are triangles. The base of a triangular pyramid is also a triangle, having four vertices (corner points) and six edges.
• The Square Pyramid has five triangle-shaped faces and a square base. It consists of five vertices (corner points). It has eight corners.

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