In geometry, a pentagonal prism is a three-dimensional form with two pentagonal bases and five rectangular faces. So, a pentagonal prism has a complete of 7 faces, 15 edges, and 10 vertices out of which 2 faces are pentagonal in shape. Us can discover the volume and also surface area that a pentagonal prism together we do for any kind of other 3D shape. Let's discover everything around pentagonal prism in detail in this article.

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 1 What is a Pentagonal Prism? 2 Properties that a Pentagonal Prisms 3 Types that Pentagonal Prisms 4 Pentagonal Prism Formulas 5 Net the a Pentagonal Prism 6 FAQs ~ above Pentagonal Prism

## What is a Pentagonal Prism?

A pentagonal prism is a three-dimensional hard that has actually two pentagonal bases - bottom and also top. All the various other sides that a pentagonal prism have actually the form of a rectangle. The is easy to know the shape of a pentagonal prism by drawing a pentagon on a piece of record using directly lines. Climate imagine it extending up from the sheet of paper. The 3D form so formed will it is in a pentagonal prism! A pentagonal prism has:

7 faces15 edges10 verticesPentagon bottom and also top

### Pentagonal Prism Examples

Here are some real-life examples of a pentagonal prism. Look at the figures given below and also look approximately you to find an ext examples of pentagonal prism and make your very own list.

U.S. Defence department HeadquarterBarns and also boxesDecorative items ## Properties of a Pentagonal Prism

A pentagonal prism is composed of miscellaneous properties that are unique to this hard shape. Noted below are some of the properties of a pentagonal prism:

The base of a pentagonal prism is in the shape of a pentagon.The sides of a pentagonal prism are shaped choose a rectangle.A pentagonal prism is a form of heptahedron, i m sorry is a polyhedron with seven plane faces.The cross-section the a pentagonal prism is a pentagon.

## Types of Pentagonal Prisms

Pentagonal prisms deserve to be categorized right into the following types:

Regular pentagonal prismsRight pentagonal prismsOblique pentagonal prisms

### Regular Pentagonal Prisms

If every the political parties of a pentagonal prism are equal in length, the is referred to as a constant pentagonal prism. Keep in mind the complying with properties that a continual pentagonal prism.

All rectangular faces of a constant pentagonal prism space congruent.When the pentagonal deals with of a consistent pentagonal prism space the bases, the rectangular faces of the prism are stated to it is in lateral.

### Right Pentagonal Prism

If the pentagon deals with of a pentagonal prism space congruent and also parallel, and also the rectangular encounters are perpendicular come the pentagon faces, the is referred to as a right pentagonal prism. ### Oblique Pentagonal Prism

If the pentagon faces of a pentagonal prism space not precisely on optimal of each other, the is, as soon as the rectangular deals with are no perpendicular come the pentagon faces, it's called an tilt pentagonal prism. ## Pentagonal Prism Formulas

The recipe of a pentagonal prism help us to discover out the surface ar area and its volume really quickly and easily. Watch the following number where 'a' is the apothem size of the prism, 'b' is the basic length, and 'h' is the elevation of the prism.

### Surface Area that a Pentagonal Prism

The surface area of a pentagonal prism offers the area the each challenge of the prism. The formula because that the surface area of a pentagonal prism is:

Surface Area = (5ab + 5bh) square units

### Pentagonal Prism Volume

The volume the a pentagonal prism offers the volume of the prism. The formula because that the volume that a pentagonal prism is:

Volume = (5/2 × abh) cubic units

Example: If the apothem size 'a' the a pentagonal prism is 5 feet, the base size 'b' is 4 feet, and the elevation 'h' is 6 feet. The surface area that the pentagonal prism is: 5ab + 5bh = (5 × 5 × 4) + (5 × 4 × 6) = 100 + 120 = 220 square feet.

The volume of the pentagonal prism is: 5/2 × abh = 5/2 × 5 × 4 × 6 = 300 cubic feet.

## Net of a Pentagonal Prism

The network of a pentagonal prism is the flattened watch of the shape. When the pentagonal prism is opened, the two forms that have the right to be seen are the rectangle and the pentagon. The net of the pentagonal prism is composed of the two pentagons which is the basic of the shape and rectangles which is the sides or deals with of the shape. ### Related short articles on Pentagonal Prism

Check out these interesting articles on the pentagonal prism. Click to know more!

Example 1: Jenifer is pack a chocolate box in the shape of a pentagonal prism. She needs wrapping record to load it. Determine the surface area of the wrapping paper needed if the size of the box room as follows:

Apothem length, a = 10 inchesBase length, b = 20 inchesHeight, h = 15 inches

Solution:

To determine the surface area that the pack paper, we require to identify the surface area the the box. The surface ar area of the box is 5ab + 5bh = (5 × 10 × 20) + (5 × 20 × 15) = 1000 + 1500 = 2500 square inches.

Therefore, the surface ar area that the wrapping file 2500 square inches.

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Example 2: Emily desires to to fill a pentagonal prism-shaped container with water. Identify the volume of the container so the Emily knows exactly how much water is needed. The dimensions of the container space as follows:

Apothem length, a = 25 feetBase length, b = 17 feetHeight, h = 15 feet

Solution:

To know the volume of the container, we require to uncover the volume that the container. The volume of the pentagonal prism-shaped container is 5/2 × abh = 5/2 × 25 × 17 × 15 =15,937.5 feet3.