# 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