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Surface area of a pyramid calculator: Use this calculator to check your work. It calculates,
  • Area of Base
  • Surface Area of Pyramid
  • Volume of Pyramid
Find the total surface area of a triangular shaped pyramid with a slant height of 16 units, base length of 8 units, and a height of 7 units.
Step 1. Find the lateral area of one side.
1/2(8 * 16 )= 64 units

Step 2. Multiply by the number of the sides.
64*3 = 192 units

Step 3. Find the area of the base
½ *( 8 * 7) = 28

Step 4. Add the lateral area and the base area together for the total surface area.
192 + 28 = 220 units squared



Slant Height =16 Units
Base Length= 8 units
7
height of pyramid
surface area of a pyramid infographic
Common Core Standard: 7.G.6   Seventh Grade Math
orange box/Geometry Tip: Slant height is not the same as the height of the pyramid.
Geometry Tip: Slant height is not the same as the height of the pyramid. The slant height is the altitude of the lateral area of the side of the pyramid. The following video details how to find slant height of a pyramid.
Slant height of a Pyramid
Questions answered in this video...

  • What is the slant height of a pyramid?
  • What is the lateral area of a pyramid?
  • How is the slant height of a pyramid  different than it's height?
  • Is slant height used to calculate total surface area of a pyramid?
Questions answered in this video...

What is the formula for finding the surface area of a pyramid?

What is slant height for a pyramid?

Is the base the same for all pyramids?

How do you find the perimeter of a pyramid?
How to find the surfave area of a pyramid
Example of finding the surface area of a pyramid
arrow pointing left
arrow pointing left

Step One: Find the lateral Area of one side of the Pyramid

Lateral Area = 1/2 b* s * number of triangular faces
b= base length
s= slant height


Slant Height = A^2+ B^2= C^2
A= 1/2 length of one side of the base
B= Center Height of the Pyramid



Step Two: Multiply the Lateral area of one side of the Pyramid by the number of sides, in order to find the Lateral Area of the entire pyramid


Step Three:  Find the area of the base, by multiplying length times width.
​                             The formula used to find the base area will depend on the                                        shape of the base. Check here for base area formulas

Step Four:  Total Surface Area = Base area + Lateral Area together 
                                                                       (step 2 + step 3)





Surface Area of a Pyramid

Use the formula 1/2 Base * Slant Height
= Total Surface Area of the Pyramid

Find the surface area of a pyramid with a base length of 6 units and a center height of 4 units
pyramid with slant height of 5 height of 4 and base length of 6
 = Slant Height
=  length of one side of the base
4 =Center Height of the Pyramid

How to find the surface area of a pyramid

​To find the surface Area of a Pyramid​ follow these four steps:

Surface Area of a Pyramid​ with a triangular base:

Step 1. Find the lateral area of one side of the pyramid,
               The formula for lateral area of a pyramid equals  1/2 base x slant height

Step 2. Multiply the area of one side of the pyramid by the number of sides in order to get the total lateral area of the pyramid.

Step 3. Find the area of the pyramid's base. This formula will vary according to the shape of the base.

List of Base area formulas

Step 4. Add the lateral area plus the base area for the surface area of the pyramid.

​Find the surface area of a pyramid with a rectangular base of 6 by 6 units and a slant height of 5 units.:

 4 squared is the center height
surface area pyramid
 3 squared is 1/2 base 

A pyramid is a three dimensional figure that has a base and an apex. The formula for finding the surface area of a pyramid will depend on the shape of the base. For example, a pyramid with a rectangular shaped base will use length x width to find the area of the base,but a pyramid with a triangular shape will use 1/2 base x height