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.

Pentagon shape 1 US

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

Pentagon shape 2 US

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.

Pentagon shape 3 US

Convex pentagon \hspace{1cm} Concave pentagon

[FREE] 2D Shape Worksheet (Grade 2 to 4)

[FREE] 2D Shape Worksheet (Grade 2 to 4)

[FREE] 2D Shape Worksheet (Grade 2 to 4)

Use this quiz to check your grade 2 to 4 students’ understanding of 2D shape. 10+ questions with answers covering a range of 2nd, 3rd and 4th grade 2D shape topics to identify areas of strength and support!

DOWNLOAD FREE
x
[FREE] 2D Shape Worksheet (Grade 2 to 4)

[FREE] 2D Shape Worksheet (Grade 2 to 4)

[FREE] 2D Shape Worksheet (Grade 2 to 4)

Use this quiz to check your grade 2 to 4 students’ understanding of 2D shape. 10+ questions with answers covering a range of 2nd, 3rd and 4th grade 2D shape topics to identify areas of strength and support!

DOWNLOAD FREE

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.

Pentagon shape 4 US

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.

Pentagon shape 5 US

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.

Pentagon shape 6 US

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

What is the pentagon shape?

What is the pentagon shape?

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

Pentagon shape 7 US

  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.

Pentagon shape 8 US

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.

Pentagon shape 9 US

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.

Pentagon shape 11 US

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.

Pentagon shape 13 US

Identify the length of each side.

Find the sum of all sides.

State your answer with correct units.

Example 5: regular pentagon

Find the perimeter of the regular pentagon below.

Pentagon shape 14 US

Identify the length of each side.

Find the sum of all sides.

State your answer with correct units.

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.

State your answer with correct units.

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?

Pentagon shape 15 US

GCSE Quiz False

Pentagon shape 16 US

GCSE Quiz False

Pentagon shape 17 US

GCSE Quiz True

Pentagon shape 18 US

GCSE Quiz False

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

 

This shape has 5 sides and 5 vertices.

 

Pentagon shape 19 US

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

Pentagon shape 20 US

GCSE Quiz False

Pentagon shape 21 US

GCSE Quiz False

Pentagon shape 22 US

GCSE Quiz False

Pentagon shape 23 US

GCSE Quiz True

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

 

This shape has 5 sides and 5 vertices.

 

Pentagon shape 24 US

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

Pentagon shape 25 US

GCSE Quiz False

Pentagon shape 26 US

GCSE Quiz True

Pentagon shape 27 US

GCSE Quiz False

Pentagon shape 28 US

GCSE Quiz False

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

 

This shape has 5 sides and 5 vertices.

 

Pentagon shape 29 US

4. Find the perimeter of the shape below.

 

Pentagon shape 30 US

100\mathrm{~in}
GCSE Quiz False

42\mathrm{~in}
GCSE Quiz False

105\mathrm{~in}
GCSE Quiz True

84\mathrm{~in}
GCSE Quiz False

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.

 

Pentagon shape 31 US

56\mathrm{~ft}
GCSE Quiz True

52\mathrm{~ft}
GCSE Quiz False

49\mathrm{~ft}
GCSE Quiz False

65\mathrm{~ft}
GCSE Quiz False

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.

 

Pentagon shape 32 US

32\mathrm{~cm}
GCSE Quiz False

37\mathrm{~cm}
GCSE Quiz True

41\mathrm{~cm}
GCSE Quiz False

35\mathrm{~cm}
GCSE Quiz False

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}


See also: Area of a pentagon

Still stuck?

At Third Space Learning, we specialize in helping teachers and school leaders to provide personalized math support for more of their students through high-quality, online one-on-one math tutoring delivered by subject experts.

Each week, our tutors support thousands of students who are at risk of not meeting their grade-level expectations, and help accelerate their progress and boost their confidence.

One on one math tuition

Find out how we can help your students achieve success with our math tutoring programs.

x

[FREE] Common Core Practice Tests (Grades 3 to 6)

Prepare for math tests in your state with these Grade 3 to Grade 6 practice assessments for Common Core and state equivalents.

40 multiple choice questions and detailed answers to support test prep, created by US math experts covering a range of topics!

Download free