February 4, 2023

Prism and Pyramid |Definition, Types and Difference between Prism and Pyramid

Prism and Pyramid

A prism is a three-dimensional geometric structure with two bases, which are often polygonal, and three or more lateral faces, which are rectangular in shape. A prism’s sides are all perpendicular to the bases, and its lateral faces are all parallelograms. The shape of a prism’s base determines its name. For instance, the base of a triangular prism is triangular, while the base of a rectangular prism is rectangular.

A pyramid is a three-dimensional geometric shape that has a base, which is usually a polygon, and triangular faces called lateral faces that meet at a single point called the apex. The sides of a pyramid are all triangles, and the lateral faces of a pyramid are all congruent isosceles triangles. Pyramids are also named based on the shape of their base. For example, a triangular pyramid has a triangular base, and a square pyramid has a square base.

Difference between Prism and Pyramid

The main difference between a prism and a pyramid is the shape of their lateral faces. A prism has rectangular lateral faces, while a pyramid has triangular lateral faces. In addition, the lateral faces of a pyramid meet at a single point called the apex, while the lateral faces of a prism are not connected in this way.

Another difference between a prism and a pyramid is the way they are named. A prism is named based on the shape of its base, while a pyramid is named based on the shape of its base and the position of its apex. For example, a triangular pyramid has a triangular base and the apex is above the base, while a triangular prism has a triangular base but the lateral faces are rectangular.

Lastly, the volume of a prism can be calculated by multiplying the area of its base by its height, while the volume of a pyramid can be calculated by multiplying the area of its base by its height and dividing the result by 3.

Different types of prism

There are several different types of prisms that are used in a variety of applications. Here are a few examples:

  1. Triangular prism: This is a three-sided prism with two congruent triangular bases and three rectangular faces. It is used in a variety of optical applications, such as in binoculars or periscopes, to refract and reflect light.
  2. Rectangular prism: This is a six-sided prism with two congruent rectangular bases and four rectangular faces. It is commonly used in geometry to study the properties of three-dimensional objects.
  3. Pentagonal prism: This is a five-sided prism with two congruent pentagonal bases and five rectangular faces. It is used in some optical applications to refract and reflect light.
  4. Hexagonal prism: This is a six-sided prism with two congruent hexagonal bases and six rectangular faces. It is used in a variety of applications, including in the construction of certain types of telescopes.
  5. Rhombic prism: This is a six-sided prism with two congruent rhomboidal bases and four rectangular faces. It is used in some optical applications to refract and reflect light.
  6. Dispersion prism: This is a triangular prism that is used to separate white light into its component colors. It is used in a variety of applications, including in spectroscopes and other scientific instruments.

Different types of prism

Different types of pyramid

There are several different types of pyramids that are distinguished based on the shape of their base and the number of faces they have. Here are a few examples:

  1. Triangular pyramid: This is a pyramid with a triangular base and four triangular faces.
  2. Square pyramid: This is a pyramid with a square base and four triangular faces.
  3. Pentagonal pyramid: This is a pyramid with a pentagonal base and five triangular faces.
  4. Hexagonal pyramid: This is a pyramid with a hexagonal base and six triangular faces.
  5. Octagonal pyramid: This is a pyramid with an octagonal base and eight triangular faces.
  6. Conical pyramid: This is a pyramid with a circular base and a pointed apex. It is also known as a cone pyramid.
  7. Double pyramid: This is a pyramid with two bases, one on top of the other. It is also known as a bipyramid.
  8. Triangular bipyramid: This is a double pyramid with two triangular bases.
  9. Square bipyramid: This is a double pyramid with two square bases.
  10. Pentagonal bipyramid: This is a double pyramid with two pentagonal bases.

Volume of prism and pyramid :
  • Volume of a prism = \boldsymbol{Area \, \, of \, \,base \, \times height}

We can fit the pyramid within the prism if we have a prism and a pyramid with equal bases and heights. In fact, when this is the case, the pyramid takes up exactly one-third of the space in the prism. This fact enables us to see a link between the volume of a prism and the volume of a pyramid when their bases and heights are equal. In other words, the volume of a pyramid is one-third that of a prism with identical height and base.

Let us now consider the volume of a pyramid. When their bases and heights are equal, a pyramid takes up 1/3 the volume of a prism. As a result, the volume of a pyramid is equal to 1/3 of the volume of a prism. So:

  • \mathbf{Volume \, \, of \, \, a\, \, pyramid = \frac{1}{3}(area \, \, of \, \, \, the\, \, base) \times height}

Comparing the Volume of Prisms and Pyramids: 

Comparing the Volume of Prisms and Pyramids

 

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