Square Pyramid - Properties, Definition, Types, Examples - Cuemath

Square Pyramid

A square pyramid characterized by a square base is a three-dimensional shape having five faces, thus called a pentahedron. The most famous example of such a square pyramid is the Great Pyramid of Giza. A pyramid is a polyhedron that has a base and 3 or greater triangular faces that meet at a point above the base (the apex). Interestingly, pyramids are named after their base, such as

• Rectangular pyramid
• Triangular pyramid
• Square pyramid
• Pentagonal pyramid
• Hexagonal pyramid

In this article, we will explore the concept of a square pyramid and its properties. We will discuss different types of square pyramids along with their formula and the net of the square pyramid for better visualization of its figure. We will solve various examples based on the concept for a better understanding.

1.	What is a Square Pyramid?
2.	Properties of a Square Pyramid
3.	Types of Square Pyramids
4.	Square Pyramid Formula
5.	Net of a Square Pyramid
6.	FAQs on Square Pyramid

What is a Square Pyramid?

A square pyramid is a three-dimensional geometric shape that has a square base and four triangular sides that are joined at a vertex. It is a polyhedron (pentahedron) with five faces. A square pyramid consists of a square base and four triangles connected to a vertex. Its base is a square and the side faces are triangles with a common vertex.

A square pyramid has three components.

• The top point of the pyramid is called the apex.
• The bottom square is called the base.
• The triangular sides are called faces.

Properties of a Square Pyramid

Let us list out the properties we have explored in the above image. All these properties are derived from the definition of a pyramid.

• It has 5 faces.
• It has 4 side faces that are triangles.
• It has a square base.
• It has 5 vertices.
• It has 8 edges.

Types of Square Pyramids

We can distinguish the square pyramids on the basis of the lengths of their edges, position of the apex, and so on. Let us discuss the different types of square pyramids.

Right square pyramid

If the apex of the square pyramid is right above the center of the base, it forms a perpendicular with the base. Such a square pyramid is called the right square pyramid.

Oblique square pyramid

If the apex of the square pyramid is not aligned right above the center of the base, the pyramid is called an oblique square pyramid.

Equilateral square pyramid

If all the triangular faces of a square pyramid have equal edges, then the square pyramid is called an equilateral square pyramid.

Square Pyramid Formula

There are formulas for square pyramids for finding the volume, height, base area, and surface area. Here you can see the formulas of the volume, total surface area (TSA), and lateral surface area (LSA) of the square pyramid.

Base Area of a Square Pyramid

Since the square pyramid has a square base, we can calculate its base area using the same formula as the area of square, which is side × side or base edge2.

Example: Assume that the base edge of a square pyramid is given as 7 units. Then, the base area of the square pyramid is: BA = 7 × 7 = 49 square units

Volume of a Square Pyramid

The formula to determine the volume of a square pyramid is: V = [(1/3)a2h]. Here, a is the length of the base and h is the perpendicular height.

Example: Assume that the height (h) and the length of the base edge (a) are 9 units and 5 units, respectively. Then, the volume of the square pyramid is:

Volume = 1/3 x 52 x 9 = 1/3 x 25 x 9 = 75 cubic units

Surface Area of a Square Pyramid

There are two types of surface areas, one is TSA (Total Surface Area), and the other is LSA (Lateral Surface Area). When we talk about its surface area, we generally refer to its total surface area (which is the sum of areas of all faces), whereas the lateral surface area is the sum of the areas of the side faces only. Consider a square pyramid of base edge 'a', height 'h', and slant 'l'.

• The formula to calculate the surface area of a square pyramid when its height h and base edge a are given: Surface Area = a2 + 2a√[(a2/4) + h2]
• The formula to calculate the surface area of a square pyramid when its slant height l and base edge a are given: Surface Area = a2 + 2al
• The formula to calculate the curved surface area or lateral surface area of a square pyramid is given as: 2a√[(a2/4)+ h2] or 2al

Example: Assume that the height h and the length of the base edge a are 9 units and 5 units, respectively.

Then, the surface area of the square pyramid is:

Surface area = (5)2 + 2 x 5 √[(52/4) + 92]

= 25 + 10 √[(25/4) + 81]

= 25 + 10√(349/4)

= 25 +10 x 9.34

= 25 + 93.4

= 118.4 square units.

Net of a Square Pyramid

The net of a square pyramid provides a flattened view of each face and the square base along with its dimensions. When placed horizontally, the net of the pyramid with a square base is seen in a 2D shape and when folded the solid shape becomes a 3D shape of a square pyramid. The net of a square pyramid has the same number of faces when it is flattened. The net of any solid shape helps in finding the surface area of that solid shape. The image below showcases the flattened view of a square pyramid with its faces and base.

Important Notes on Square Pyramid

• A square pyramid is a three-dimensional geometric shape that has a square base and four triangular sides that are joined at a vertex.
• Surface Area of Square Pyramid = a2 + 2a√[(a2/4) + h2]
• LSA of Square Pyramid = 2a√[(a2/4)+ h2] or 2al

Related Articles

• Volume of a Right Square Pyramid
• Surface Area of Square Pyramid Calculator
• Volume of Pyramid