Formula Math Of Pentagonal Pyramid

Area of Base [ A ]= [ 5/2 ]a.s

Surface Area of Pyramid = [ 5/2 ]a.s + [ 5/2]s.l = A + [ 5/2 ]s.l

Volume of Pyramid = [ 5/6 ]a.b.h

Note :

s = side, h = height , l = length,

a = apothem ,b = lant height

### Example

Question : Find the surface area and volume of a pentagonal pyramid with the given apothem length 2, side 3, height 4 and the slant height 5.

Answer : Find the area of the base.

Solution : Area of the base [A] = [ 5/2 ]a.s = 5/2 . 2 . 3 = 15.

Answer : Find the surface area of pyramid.

Solution : Surface Area of Pyramid = A + [ 5/2 ]s.l = 15 + [5/2] .3 . 5) = 15 + [5/2 x 15] = 15 + 37.5 = 52.5.

Answer : Find the volume of pyramid.

Solution :Volume of Pyramid = [ 5/6 ].a.b.h = [5/6] . 2 . 3 x 4 = (0.833) . 24 = 20.

That is example will clearly how to calculate the Volume by Formula Math Surface Area of a Pentagonal Pyramid.