# Square Pyramid: Definition & Properties

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• 0:01 Example of a Square Pyramid
• 0:28 Definition and Properties
• 1:46 Formulas for Square Pyramids
• 3:10 Lesson Summary

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Lesson Transcript
Instructor: Karin Gonzalez

Karin has taught middle and high school Health and has a master's degree in social work.

This lesson provides an informative overview of the properties of square pyramids. Along with providing the definition for a square pyramid, the lesson includes the formulas for finding base area, volume, and surface area.

## Example of a Square Pyramid

You need not travel to Egypt to know that it hosts some of the world's most marvelous wonders: the Pyramids of Giza. These pyramids were built between 2589 and 2504 BC, so it is a true wonder that they still stand strong and tall today in the expansive desert just outside of Cairo. The Pyramids of Giza are one of oldest examples of square pyramids.

## Definition and Properties

Like all pyramids, square pyramids share the property of being a polyhedron with a polygonal base and triangular sides reaching up towards a point, called an apex. A polyhedron is a three-dimensional figure with flat polygons as sides, and a polygon is a flat, enclosed, plane shape with at least three sides and angles.

From this information it can be concluded that not all pyramids are square pyramids. All pyramids are named after their base. So, a square pyramid is a pyramid with a square base, four triangular sides, five vertices, and eight edges.The base of this pyramid is a square, and the top point is the apex.

It was mentioned that a square pyramid is a polyhedron. But to be more specific, it could be called a pentahedron because it is a polyhedron that has five sides. Remember that penta means five in Latin.

If all triangular sides of the square pyramid are equilateral, meaning each triangle has equal sides and angles, then all the edges of the square pyramid will be equal in length. This is actually called a Johnson solid. Other geometric forms can also be Johnson solids if they are convex polyhedrons with regular polygon faces but not uniform.

## Formulas For Square Pyramids

There are formulas for calculating the base area, volume, and surface area of a square pyramid. First, study the diagram and look closely at how each dimension is labeled:

The dimensions of a square pyramid are as follows:

a = base side length
e = lateral side length
h = height
s = slant height

Finding the base area of a square pyramid is simple, since it is finding the area of a square. If a is an edge of the base, then the formula to find base area of a square pyramid would be:

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