# Surface Area of a Pyramid - Lateral Area - Geometry | Summary and Q&A

172.7K views
January 3, 2018
by
The Organic Chemistry Tutor
Surface Area of a Pyramid - Lateral Area - Geometry

## TL;DR

Learn how to find the total surface area of a square based pyramid by calculating the area of the base and the lateral area.

## Install to Summarize YouTube Videos and Get Transcripts

### Q: How do you calculate the surface area of a square based pyramid?

The surface area of a square based pyramid is calculated by finding the area of the base (squared side length) and the lateral area (sum of the areas of the four triangles formed by the sides and height).

### Q: What is the formula for calculating the area of a triangle in the pyramid?

The formula for calculating the area of a triangle in the pyramid is half the product of the base and the height of the triangle.

### Q: How do you find the slant height of the triangles in the pyramid?

The slant height of the triangles can be found using the Pythagorean theorem, where the legs of the triangle are the side length (half of the base) and the height of the pyramid.

### Q: What is the total surface area formula for a pyramid?

The total surface area of a pyramid is calculated by adding the area of the base to the lateral area, which is the sum of the areas of the four triangles.

## Summary & Key Takeaways

• To calculate the surface area of a square based pyramid, calculate the area of the base (squared side length) and the lateral area (sum of the areas of the four triangles).

• Use the Pythagorean theorem to find the slant height of the triangles formed by the sides and the height of the pyramid.

• The area of each triangle is half the product of the base and the height.

• Add the area of the base and the lateral area to find the total surface area of the pyramid.