Geometry

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# Surface Area of a Pyramid

## 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.

### Example Problems

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:

SA = 2hb + b^{2}

SA = 2(20)(10) + 10^{2} = 400 + 100 = 500

2.) **The surface area is 500.**

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:

SA = 2hb + b^{2}

SA = 2(20)(5) + 5^{2} = 200 + 25 = 225

2.) **Reducing the edge length from 10 to 5 reduced the surface area from 500 to 225.**