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 + 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

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 + b2
SA = 2(20)(10) + 102 = 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 + b2
SA = 2(20)(5) + 52 = 200 + 25 = 225
2.) Reducing the edge length from 10 to 5 reduced the surface area from 500 to 225.

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