We will work with regular pyramids, in which the triangular sides are

congruent and the

base is a regular polygon. In order to solve problems which require application of the

volume and

surface area for pyramids, it is necessary to

- Surface area of a regular pyramid = area of base +

- Volume of a pyramid = .

- know how to find the area of a base:

- for a regular polygon: A =

- for a hexagonal base: A =

A typical problem involving the

volume or

surface area of a pyramid gives us one or more of the volume, lateral area,

area of a base,

height and/or

radius of the pyramid. We need to calculate some of these quantities given information about the others.

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.

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,

A = s

^{2} =

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*
*
*

where MB =

because it is half of one

side