Right Pyramid Volume and Surface Area

sides

4

height

8

length

2

base area	4.000
× height / 3	2.667
= volume	8.378

sides × length / 2	4.000
× slant height	8.062
= slant surface area	32.249

total surface area	36.249

Let

P

be a regular polygon with

n

sides of length

l

and let

A

, the apex, be a point directly above the center of

P

. A right pyramid is the solid formed by joining the vertices of

P

to

A

and filling in the triangular faces.

The Indian mathematician Aryabhata determined that the volume of any pyramid is

1

3

bh

, where

b=

2

l

n

4

cot

π

n

is the area of the base polygon

P

, using that the inner radius of

P

is

r=

l

2

cot

π

n

.

The slant height is

s=

2

h

+

2

r

. The base perimeter is

p=nl

, number of sides×side length. The slant surface area is given by

Ps

2

=

nls

2

.