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Types of angles Lines Addition and subtraction Adding decimalsHere 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.

**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

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 FREEUse 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 FREEPentagon 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.

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+sOr 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}

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.

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

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

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

**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.

2**State whether or not the shape is a pentagon.**

This shape is not a pentagon.

3**If 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.

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

**Look for the characteristics of a pentagon shape.**

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

This shape has 5 sides and 5 vertices.

**State whether or not the shape is a pentagon.**

This shape is an irregular pentagon.

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

**Look for the characteristics of a pentagon shape.**

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

This shape has 5 sides and 5 vertices.

**State whether or not the shape is a pentagon.**

This shape is an irregular pentagon.

In order to find the perimeter of a pentagon shape,

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

Find the perimeter of the pentagon below.

**Identify the length of each side.**

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

P=s+s+s+s+s

**Find the sum of all sides.**

\begin{aligned}P&=15+12+15+12+11 \\\\
P&=65 \end{aligned}

**State your answer with correct units.**

The perimeter is 65\mathrm{~cm}.

Find the perimeter of the regular pentagon below.

**Identify the length of each side.**

The pentagon shown is a regular pentagon so all sides have an equal measure, 25\mathrm{~inches}. You can use the formula,

P=s\times{5}

**Find the sum of all sides.**

\begin{aligned}P&=s\times{5} \\\\
P&=25 \times{5} \\\\
P&=125 \end{aligned}

**State your answer with correct units.**

The perimeter is 125\mathrm{~inches}.

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.**

The pentagon mentioned is a regular pentagon so all sides have an equal measure, 13\mathrm{~inches}. You can use the formula,

P=s \times 5

**Find the sum of all sides.**

\begin{aligned}P&=s\times{5} \\\\
P&=13\times{5} \\\\
P&=65 \end{aligned}

**State your answer with correct units.**

Sarah will need 65\mathrm{~feet} of fencing.

- 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.

**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.

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}

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

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

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

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

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

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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!