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# Surface Area of a Pyramid

## Common Core Standard: 7.G.6 Seventh Grade Math

• What is the slant height of a pyramid?
• What is the lateral area of a pyramid?
• How is the slant height of a pyramid  different than it’s height?
• Is slant height used to calculate total surface area of a pyramid?

A pyramid is a three dimensional figure that has a base and an apex. The formula for finding the surface area of a pyramid will depend on the shape of the base. For example, a pyramid with a rectangular shaped base will use length x width to find the area of the base,but a pyramid with a triangular shape will use 1/2 base x height

### Surface Area of a Pyramid​ with a triangular base:

Step 1. Find the lateral area of one side of the pyramid,
The formula for lateral area of a pyramid equals  1/2 base x slant height

Step 2. Multiply the area of one side of the pyramid by the number of sides in order to get the total lateral area of the pyramid.

Step 3. Find the area of the pyramid’s base. This formula will vary according to the shape of the base.

Step 4. Add the lateral area plus the base area for the surface area of the pyramid.

Geometry Tip: Slant height is not the same as the height of the pyramid. The slant height is the altitude of the lateral area of the side of the pyramid. The following video details how to find slant height of a pyramid.