List of Pyramid Formula – Surface Area, Volume of Pyramid

The first thing that comes to mind with the word Pyramid is the Great Pyramid of Egypt. If you look at the image of the historical Pyramid then its base is actually a square. So, it is taken as a square pyramid and another popular form of the pyramid is Triangular Pyramid. So, what is Pyramid exactly? Let us understand the Pyramid concept in-depth throughout the article.

What is Pyramid?

A pyramid is a three-dimensional shape that has three sides and one polygon base. At the same time, a triangular pyramid has a triangle base with three triangular faces. This type of pyramid can have four vertices and six edges.

Other than square or triangular Pyramids, the other popular types are rectangular, hexagonal, pentagonal, regular or irregular polygon etc. Most of them are named after their base. For example, in case of a regular pyramid, the base would be regular otherwise it is irregular.

Type of Pyramid

  1. Triangular Pyramid
  2. Square Pyramid
  3. Pentagonal Pyramid
  4. Right pyramid
  5. Oblique pyramid

Let us have a quick look at components of Pyramid before we discuss on Pyramid formulas. The first component is based, second is faces (3 triangles), and the last is apex where all three faces meet. The other important measurements related to triangular pyramids are height, length, base length, or slant height etc. you should have a deep understanding of each of the terms before you start solving complex pyramid problems.

List of Basic Pyramid Formulas

There are complex pyramid problems where you need to calculate base area, slant height or perimeter etc. So, how it could be possible? This is possible by a deep understanding of basic Pyramid Formulas that allows you to get a deep understanding of Pyramid based on different parameters.

You can calculate the volume or surface area of any pyramid instead of its shape or type. There are few problems related to the prism in physics then you can work on those problems with Pyramid formulas and equations.

To find out the surface area and some formulas can be used. The surface area of a pyramid is the total area of all the surfaces that pyramid has. Formulas to find out the surface area of a pyramid.

Pyramid

\[\large Surface\;Area\;of\;a\;Pyramid\]

\[\large =Base\;Area+\frac{1}{2}\left(Number\;of\;Base\;Sides \times Slant\;Height \times Base \;Length \right)\]

\[\large Volume\;of\;a\;Pyramid=\frac{1}{2} \times Base\;Area \times Height\]

Square Pyramid

A Pyramid with a square base, 4 triangular faces and an apex is a square pyramid.

Square Pyramid

The Square Pyramid formulas are,

\[\large Base\;Area\;of\;a\;Square\;Pyramid=b^{2}\]

\[\large Surface\;Area\;of\;a\;Square\;Pyramid=2bs+b^{2}\]

\[\large Volume\;of\;a\;Square\;Pyramid=\frac{1}{3}b^{2}h\]

Where,
b – base length of the square pyramid.
s – slant height of the square pyramid.
h – height of the square pyramid.

Triangular Pyramid

Triangular pyramid is said to the pyramid where it has triangular faces, triangular.

The Triangular Pyramid formulas are,

\[\large Base\;Area\;of\;a\;Triangular\;Pyramid=\frac{1}{2}\:ab\]

\[\large Surface\;Area\;of\;a\;Triangular\;Pyramid=\frac{1}{2}\:ab+\frac{3}{2}\:bs\]

\[\large Volume\;of\;a\;Triangular\;Pyramid=\frac{1}{6}\:abh\]

Where,
a – apothem length of the triangular pyramid.
b – base length of the triangular pyramid.
s – slant height of the triangular pyramid.
h – height of the triangular pyramid.

Pentagonal Pyramid

This pyramid has pentagonal base, with 5 sides , triangular faces and an apex.

Pentagonal PyramidThe Pentagonal Pyramid Formulas are,

\[\large Base\;Area\;of\;a\;Pentagonal\;Pyramid=\frac{5}{2}\:ab\]

\[\large Surface\;Area\;of\;a\;Pentagonal\;Pyramid=\frac{5}{2}\:ab+\frac{5}{2}\:bs\]

\[\large Volume\;of\;a\;Pentagonal\;Pyramid=\frac{5}{6}\:abh\]

Where,
a – apothem length of the pentagonal pyramid.
b – base length of the pentagonal pyramid.
s – slant height of the pentagonal pyramid.
h – height of the pentagonal pyramid.

Hexagonal Pyramid

This pyramid has a hexagonal base with six sides, six triangular faces and an apex.

Hexagonal Pyramid

The Hexagonal Pyramid Formulas are,

\[\large Base\;Area\;of\;a\;Hexagonal\;Pyramid=3ab\]

\[\large Surface\;Area\;of\;a\;Hexagonal\;Pyramid=3ab+3bs\]

\[\large Volume\;of\;a\;Hexagonal\;Pyramid=abh\]

Where,
a – apothem length of the hexagonal pyramid.
b – base length of the hexagonal pyramid.
s – slant height of the hexagonal pyramid.
h – height of the hexagonal pyramid.

Pyramid Problem with Solution

To solve pyramid problems, this is necessary to learn analogical reasoning otherwise mathematics will just be a list of rules and formulas that can be difficult to understand by anyone. To find the solution of a Pyramid problem, if you search analogically then you could engage yourself in relevant mathematical discussion and get a deeper understanding of the concept.

Why should students learn Pyramid Formulas?

Students need to learn different mathematical concepts during their early school and college studies too. One of the common topics is Pyramid that is applicable to various real-life problems too. Also, students can appear for various competitive exams once they are sure on different mathematical concepts and terminologies.

With a clear understanding of Pyramid Formulas, this is possible to gain meaningful insights for real-life pyramids, how they were formed and volume, surface area or slant height etc. It is further used in different domains like science, engineering, physics, and more.


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