# Pentagon shape

Here you will learn about the pentagon shape, including how to identify a pentagon shape and how to find the perimeter of regular pentagons.

Students will first learn about the pentagon shape as a part of geometry in 2 nd grade, and will continue expanding on this topic throughout elementary school.

## What is the pentagon shape?

A pentagon shape is a five-sided polygon that has five straight sides, five vertices and five equal interior angles. There are different types of pentagons.

A regular pentagon is a geometric shape with 5 equal sides that are equal length and equal internal angle measures.

An irregular pentagon has 5 sides that are not all equal, and 5 interior angles that are not all equal.

There are convex pentagons and concave pentagons. A convex pentagon is a pentagon that has all vertices that point outward. A concave pentagon is a pentagon where one or more of the vertices points inwards.

Convex pentagon \hspace{1cm} Concave pentagon

### Other properties of a pentagon shape

Pentagon shapes have both interior and exterior angles. A pair of interior and exterior angles of all polygons add to 180^{\circ} because they form a straight line. They are supplementary angles.

Interior angles of a pentagon are the angles inside the 2D shape, formed when two sides of the shape meet. The sum of the interior angles of any pentagon is 540^{\circ}.

Exterior angles of a pentagon are the angles between the pentagon and the extended line from the next side. The sum of the exterior angles of any polygon is always 360^{\circ}.

A regular pentagon has 5 lines of symmetry, or diagonals, one through each vertex and midpoint.

### Perimeter of a regular pentagon shape

The perimeter is the sum of the lengths of its five sides.

To find the perimeter of a pentagon shape, you can use the following formula:

P=s+s+s+s+s

Or for regular pentagons, you can use:

P=s\times{5}

For example, find the perimeter of the regular pentagon.

\begin{aligned}P&=s\times{5} \\\\ P&=4\times{5} \\\\ P&=20\mathrm{~inches} \end{aligned}

## Common Core State Standards

How does this relate to 2 nd grade math, 3 rd grade math, 4 th grade math, and 5 th grade math?

• Grade 2: Geometry (2.G.A.1)
Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

• Grade 3: Measurement and Data (3.MD.D.8)
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

• Grade 4: Geometry (4.G.A.2)
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

• Grade 5: Geometry (5.G.A.3)
Understand that attributes belonging to a category of two dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

## How to identify a pentagon shape

In order to identify a pentagon shape, you need to:

1. Look for the characteristics of a pentagon shape.
2. State whether or not the shape is a pentagon.
3. If the shape is not a pentagon, explain what characteristics are different.

## Pentagon shape examples

### Example 1: identifying pentagon shapes

Look at the image below and determine if it’s a pentagon shape or not

1. Look for the characteristics of a pentagon shape.

A pentagon shape is a 5 sided shape with 5 vertices.

This shape has 6 sides and 6 vertices.

2State whether or not the shape is a pentagon.

This shape is not a pentagon.

3If the shape is not a pentagon, explain what characteristics are different.

This shape is not a pentagon because it has more than 5 sides and 5 vertices. This shape is a hexagon.

### Example 2: identifying pentagon shapes

Look at the image below and determine if it’s a pentagon shape or not.

Look for the characteristics of a pentagon shape.

State whether or not the shape is a pentagon.

### Example 3: real-life example

Look at the image below and determine if it’s a pentagon shape or not.

Look for the characteristics of a pentagon shape.

State whether or not the shape is a pentagon.

## How to find the perimeter of a pentagon shape

In order to find the perimeter of a pentagon shape,

1. Identify the length of each side.
2. Find the sum of all sides.
3. State your answer with correct units.

### Example 4: irregular pentagon

Find the perimeter of the pentagon below.

Identify the length of each side.

Find the sum of all sides.

### Example 5: regular pentagon

Find the perimeter of the regular pentagon below.

Identify the length of each side.

Find the sum of all sides.

### Example 6: perimeter of pentagon shape word problem

Sarah is designing a decorative fence for her garden in the shape of a regular pentagon. Each side of the pentagon measures 13\mathrm{~feet}. What is the total length of fencing she will need?

Identify the length of each side.

Find the sum of all sides.

### Teaching tips for pentagon shape

• While worksheets have their place within the classroom, for this particular topic, consider incorporating more hands-on activities or interactive lessons.

• Show students real-life examples, such as The Pentagon in Washington D.C, which houses the department of defense, or the shape of the vegetable okra when cut.

• Encourage collaboration between students by providing problem-solving tasks that involve pentagon shapes. Students working together encourages communication, teamwork and critical thinking skills.

### Easy mistakes to make

• Mistaking pentagon shapes with a different shape
Students may try to “eyeball” shapes to identify them. Encourage students to follow a set of steps, including counting the number of sides a shape has, to ensure they are identifying the correct shape.

• Confusing interior and exterior angles
Students may unintentionally mix up the meaning of interior (those inside a shape) and exterior angles (those outside the shape) within pentagons. Providing visuals, whether within the classroom, in a math journal or in an online classroom, is a way to reinforce the meaning of these angles.

• Using the wrong formulas
Students will learn how to find the perimeter of many different shapes. Instead of reinforcing students memorizing the formula, reinforce what perimeter is and how to find it. Once students understand that perimeter is adding all the sides up, they won’t need to memorize a formula.

### Practice pentagon shape questions

1. Which of the following is an example of a pentagon shape?

A pentagon shape is a 5 sided shape with 5 vertices.

This shape has 5 sides and 5 vertices.

2. Which of the following is an example of a pentagon shape?

A pentagon shape is a 5 sided shape with 5 vertices.

This shape has 5 sides and 5 vertices.

3. Which of the following is an example of a pentagon shape?

A pentagon shape is a 5 sided shape with 5 vertices.

This shape has 5 sides and 5 vertices.

4. Find the perimeter of the shape below.

100\mathrm{~in}

42\mathrm{~in}

105\mathrm{~in}

84\mathrm{~in}

The pentagon shown is a regular pentagon so all sides have an equal measure, 21\mathrm{~in}.  You can use the formula P=s \times 5.

\begin{aligned}P&=s\times{5} \\\\ P&=21\times{5} \\\\ P&=105 \mathrm{~in} \end{aligned}

5. Find the perimeter of the shape below.

56\mathrm{~ft}

52\mathrm{~ft}

49\mathrm{~ft}

65\mathrm{~ft}

The lengths of the sides are different, so you will use the formula

P=s +s+s+s+s.

\begin{aligned}P&=14+11+14+8+9 \\\\ P&=56\mathrm{~ft} \end{aligned}

6. Find the perimeter of the pentagon below.

32\mathrm{~cm}

37\mathrm{~cm}

41\mathrm{~cm}

35\mathrm{~cm}

The lengths of the sides are different, so you will use the formula

P=s +s+s+s+s.

\begin{aligned}P&=7+9+7+5+9 \\\\ P&=37\mathrm{~cm} \end{aligned}

## Pentagon shape FAQs

What is the meaning of the word pentagon?

The prefix “penta-” comes from the Greek word “pente” which means 5. The suffix “-gon” comes from the Greek word “gonia”, which means angle.

What is the shape of a pentagon?

A pentagon is a five-sided shape with five angles. If the sides of the pentagon are all equal, it is a regular pentagon.

What is an equilateral pentagon?

Equilateral pentagon have five sides that are equal in length, and five interior angles are congruent. They are a subset of regular pentagons.

How do you find the area of a pentagon?

The area of a regular pentagon can be calculated by using the area of the pentagon formula:

\text{Area of a pentagon }= \cfrac{1}{2} \, \times \text{ perimeter } \times \text{ apothem}

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