## Surface Area of a Pyramid Lesson

### 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 + b ^{2}**

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

INTRODUCING

### 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:

- Plugging what we know into the formula, we get:
- SA = 2hb + b
^{2} - SA = 2(20)(10) + 10
^{2}= 400 + 100 = 500 **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:

- Plugging the edge length of 5 and height of 20 into the formula, we get:
- SA = 2hb + b
^{2} - SA = 2(20)(5) + 5
^{2}= 200 + 25 = 225 **Reducing the edge length from 10 to 5 reduced the surface area from 500 to 225.**