Pharaoh Wants To Know....Pyramid Math

Made famous by the ancient Pharaohs centuries ago, pyramids are shapes that have taken their place in history.  The Pyramids of Giza are one of the ancient wonders of the world.  With the centuries of time and weather, they have been proven to be some of the sturdiest man-made structures in the history of man-kind.  With all the pressures of designing one of the most important structures in human history, what kind of math did the ancient engineers need to know?

Well, perhaps they started with volume and area.

Before determining the volume or area, we first need to determine what type of pyramid we are working with.  Pyramids can have many different variations.  Usually there are two ways to classify a pyramid.  First is the base.  Many pyramids, like the Pyramids of Giza, are square base pyramids, but the base can also be a triangle, rectangle, pentagon, etc.  As long as the base has at least 3 sides, it can stand upright.  All pyramids have triangular sides that meet at a point on top.  However, a pyramid that has the top point directly over the center of the base will have equal triangular sides all around and is referred to as a “regular” pyramid.  If the top point is not over the center of the base and not all of the sides are the same, this is an “irregular” pyramid. The Pyramids of Giza are square regular pyramids with all of the triangular sides of equal shape, and the top point directly over the center of the square base.

Determining the surface area of a pyramid is fairly basic.  To determine the total surface area, you simply add the individual areas of the lateral sides and the base.  On a square regular pyramid, like the Pyramids of Giza, you would add the areas of the 4 individual triangular sides and the base.  On a regular triangular pyramid, you would add the areas of the 3 individual triangular sides with the area of the base.

To learn more about the calculation of the surface area of a regular square pyramid or a regular triangular pyramid, follow these links:

Surface Area Regular Square Pyramid               Surface Area Regular Triangular Pyramid

When the ancient engineers were thinking about how much material was needed to build the massive pyramids, they most likely needed to determine the volume.  The first step to determining the volume of a pyramid is still to identify what type of pyramid you are working with.  Once you have determined the type, find the area of the base and multiply the base area by 1/3^rd of the total pyramid height.

To learn more about the calculation of the volume of pyramids, follow this link:

Pyramid Volume Calculator

So when it’s time for you to build a new home, maybe you should look into building a pyramid.  After all, it may last longer than you.

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