# Pentagonal Pyramid Tutorial

## Pentagonal Pyramid Tutorial

##### Pentagonal Pyramid Definition:

A Pentagonal Pyramid is a pyramid with a pentagonal base.

#### Pentagonal Pyramid Formula :

Area of Base(A) = (5/2)as Surface Area of Pyramid = (5/2)as + (5/2)sl = A + (5/2)sl Volume of Pyramid = (5/6)abh
###### where
a = apothem length, s,b = side, h = height and l = slant height
##### Pentagonal Pyramid Image/Diagram ##### Case 1:

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.

###### Step 1:

Find the area of the base. Area of the base(A) = (5/2)as = 2.5 * 2 * 3 = 15.

###### Step 2:

Find the surface area of pyramid. Surface Area of Pyramid = A + (5/2)sl = 15 + ((5/2) * 3 * 5) = 15 + (2.5 * 15) = 15 + 37.5 = 52.5.

###### Step 3:

Find the volume of pyramid. Volume of Pyramid = (5/6)abh = (5/6) * 2 * 3 * 4 = (0.833) * 24 = 20. The above example will clearly illustrates how to calculate the Volume, Surface Area of a Pentagonal Pyramid manually.

#### Related Calculator:

This tutorial will help you dynamically to find the Math area problems.