Pyramid

A pyramid is defined as a three-dimensional structure encompassing a polygon as its base. You must have heard about The Great Pyramid of Giza, which is structured in the same concept. Every corner of this structure is linked to a single apex which makes it appear as a distinct shape. The edge of each base and it’s top makes a triangle. In Maths, you will learn this geometrical shape and its properties along with the formulas for pyramids to find surface area and volumes.

 

Pyramid

Types Of Pyramids

There are different types of pyramids that are named based on the shapes of their bases.

  • Triangular Pyramid
  • Square Pyramid
  • Pentagonal Pyramid
  • Right Pyramid
  • Oblique Pyramid

Triangular Pyramid

The base of this pyramid has a shape of a triangle, therefore we call it as a triangular pyramid.

Triangular Pyramid

Square Pyramid

The base of this type of pyramids has a shape of a square, therefore we call it as a Square Pyramid.

Square Pyramid

Pentagonal Pyramid

The base of this one has a shape of a Pentagon, therefore we call it as a Pentagonal Pyramid.

Pentagonal Pyramid 

Right Pyramid

This apex of this pyramid is exactly over the middle of the base, hence named as Right Pyramid.

Right Pyramid 

Oblique Pyramid

The apex of this pyramid is not exactly over the middle of its base and named as Oblique Pyramid.

Oblique Pyramid

Regular vs Irregular Pyramid

To distinguish between regular and irregular Pyramid, you need to consider the shape of the base. If the base of a polygon is regular, it’s labeled as Regular Pyramid, else it is considered as Irregular Pyramid. You can see the figures given below for both the pyramids

Regular PyramidRegular Pyramid                              Irregular Pyramid  Irregular Pyramid

                    Regular                                                                                       Irregular

Pyramid Formulas

To find out the surface area and volumes of pyramids, some formulas can be used. The surface area of a pyramid is the total area of all the surfaces, including the base area, perimeter and slant height, such as;

Surface Area = (base area) + (1/2) × (perimeter) × (slant height)

To calculate the volume, the formula is;

Volume = 1/ 3 × (Base Area) × height

Note: Base area is the area of the base of the pyramid, which will vary based on its types.

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Practise This Question

Solve the following pair of equations:
1x+3y=1
6x12y=2
(where x0,y0)