Pyramid Surface Area Formula

A right square pyramid has a square-shaped base and 4 congruent triangle faces. The formula for surface area of a right square pyramid is given as:

SA = 2hb + b²

Where SA is the surface area, h is the height of the triangular face, and b is the edge length of the square base.

Surface Area of a Pyramid Example Problems

Let's go through a couple of example problems together to practice finding the surface area of a pyramid.

Example Problem 1

Find the surface area of a right square pyramid with an edge length of 10 and a triangle face height of 20.

Solution:

1. Plugging what we know into the formula, we get:
2. SA = 2hb + b²
3. SA = 2(20)(10) + 10² = 400 + 100 = 500
4. The surface area is 500.

Example Problem 2

If the pyramid from problem 1 has its edge length reduced from 10 to 5, how does the surface area change?

Solution:

1. Plugging the edge length of 5 and height of 20 into the formula, we get:
2. SA = 2hb + b²
3. SA = 2(20)(5) + 5² = 200 + 25 = 225
4. Reducing the edge length from 10 to 5 reduced the surface area from 500 to 225.