# Pentagonal Prism Tutorial

## Pentagonal Prism Tutorial

##### Pentagonal Prism Definition:

The pentagonal prism is a prism having two pentagonal bases and five rectangular sides.

#### Pentagonal Prism Formula :

Area of Base(A) = ½ * a * 5 * s
Perimeter of Base(P) = 5s
Surface Area of Prism = 5as + 5sh = 5as + Ph
Volume of Prism = (5/2)ash = Ah
###### where

a = apothem length, s = side, h = height.
##### Pentagonal Prism Image/Diagram

##### Pentagonal Prism Example :

##### Case 1:

Find the surface area and volume of a pentagonal prism with the given apothem length 2, side 3 and height 4.

###### Step 1:

Find the area of the base.
Area of the base(A) = ½ * a * 5 * s = 0.5 * 2 * 5 * 3 = 15.

###### Step 2:

Find the perimeter of the base.
Perimeter of the base(P) = 5s = 5 * 3 = 15.

###### Step 3:

Find the surface area of prism.
Surface Area of Prism = 5as + Ph = (5 * 2 * 3) + (15 * 4) = 30 + 60 = 90.

###### Step 4:

Find the volume of prism.
Volume of Prism = Ah = 15 * 4 = 60.
The above example will clearly illustrates how to calculate the Volume, Surface Area, Perimeter of a Pentagonal Prism manually.

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