• know how to use basic formulas for volume and surface area of a regular pyramid:
  
  

1. Surface area of a regular pyramid = area of base +
   
   
2. Volume of a pyramid = .
   
   

• know how to find the area of a base:
  
  

1. for a regular polygon: A =
   
   
2. for a hexagonal base: A =
   
   

• know how to find the length of a side of a regular polygon using .
  
  
• use the Pythagorean Theorem in finding the radius, side of a base, or slant height.
  
  

To get started, we must determine which quantities are known and look at the formulas available for our use to to see which additional variables we need to calculate.

 

For both surface area and volume, we need the area of the square base.

 

It is usually easier to find the area of the base if we first know the length of one side. Since triangle ACB is a right triangle with hypotenuse 5 and one leg 3, our square base has a radius of 4 . We can now use the formula

 

 

 

along with the knowledge that the radius r = 4 and the number of sides n = 4 to find the length of one side of the square,

 

 

 

We now know the area of the square base is

 

A = s² =

 

We can use this to find the volume which is

 

V =

 

To find the surface area, we need the perimeter of the base, P, and the slant height, s

 

surface area = area of base + 

 

The perimeter of our square base is just four times the length of one side:

 

perimeter = 4()

perimeter =

 

The slant height is the length of AM in triangle ABD. Using the Pythagorean Theorem and triangle ABM,

 

where MB = because it is half of one side

 

The surface area equals .