Right Pyramid Volume and Surface Area
Right Pyramid Volume and Surface Area
Let be a regular polygon with sides of length and let , the apex, be a point directly above the center of . A right pyramid is the solid formed by joining the vertices of to and filling in the triangular faces.
P
n
l
A
P
P
A
The Indian mathematician Aryabhata determined that the volume of any pyramid is bh, where is the area of the base polygon , using that the inner radius of is .
1
3
b=cot
2
l
n
4
π
n
P
P
r=cot
l
2
π
n
The slant height is . The base perimeter is , number of sides×side length. The slant surface area is given by =.
s=+
2
h
2
r
p=nl
Ps
2
nls
2