WOLFRAM|DEMONSTRATIONS PROJECT

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
.