Find your Math Personality!

Closed Shapes

Closed Shapes

In geometry, there are two types of 2-Dimensional shapes: open shapes and closed shapes.

Think about the difference in the shape of a circle and a semi-circle.

shape of a circle and a semi-circle

A circle forms a closed shape, while a semi-circle forms an open shape, right?

In this mini-lesson, we will explore the world of shapes by learning about the definition of closed shapes and open shapes, examples of closed shapes, the difference between open and closed shapes with the help of interesting simulation, some solved examples, and a few interactive questions for you to test your understanding.

Lesson Plan

What Is the Definition of Closed Shapes?

Carefully observe the shapes of letters C and D.

English alphabets C and D

Have you noticed the basic difference in the shapes of the above letters?

Letter C forms an open shape, while letter D forms a closed shape.

Definition of Closed Shapes

Any enclosed shape that does not have any open ends and can be traced back from where it started without any break is known as a closed shape.

Some examples of closed shapes are shown below:

Closed shapes

Closed Shapes in Geometry

  • A triangle is a closed figure with 3 sides and 3 vertices.

A triangle

  • A circle is a closed shape with no sides, no vertices, and one face.

A circle is a closed shape

  • A quadrilateral is a closed shape with 4 sides and 4 vertices. Examples of a quadrilateral are square, rectangle, rhombus, parallelogram, trapezium, etc.

A quadrilateral is a closed shape

  • A pentagon is a closed shape with 5 sides and 5 vertices.

A pentagon is a closed shape

  • A hexagon is a closed shape with 6 sides and 6 vertices.

A hexagon is a closed shape

There are many other closed shapes in geometry apart from the ones that are mentioned above, for example, heptagon, octagon, decagon, oval, etc.

Closed shapes made up of straight lines are known as polygons.

What Are the Examples of Closed Shapes?

In geometry, you have seen examples of closed shapes in the above section.

Now, let us look at some real-life examples of closed shapes.

cloud shape

road sign board

star shape

While drawing a cloud, signboard, and a star, we usually choose to represent them in a closed shape. 

Let us think about the English alphabet.

Can you think of more examples of closed shapes from English alphabets?

Yes. Letter B, letter D, letter O are some examples of closed shapes.

English alphabets as closed shapes

tips and tricks
Tips and Tricks
  1. To identify whether a given shape is closed or not, try to trace it with a pencil and see if you can reach the starting point again without leaving any side and without any break.

What Is an Open Shape?

Any shape in which the start point and the endpoint is different and not connected is called an open shape. 

Open shapes are not continuous and cannot be traced without any break.

Some examples of open shapes are given below:

open shapes

What is the difference between open and closed shapes?

Considering the definition of open and closed shapes, the difference between the two is tabulated below:

Open Shapes Closed Shapes
Open shapes have a gap or gaps in between. Closed shapes have no openings or gaps.
Sides of an open shape do not meet. Sides of closed shapes can be traced from start to finish.
Example- A skipping rope Example- A hula-hoop

Now, try your hands at the simulation given below and mark closed shapes and open shapes correctly.

Challenge your math skills
Challenging Question
  1. Look at the shape given below. There are no openings in the shape, right? But, while drawing this shape, after drawing one circle we have to lift our pencil and choose another starting point to draw the second circle. 

          So, should we consider it as a closed shape or not?

is it closed or open shape

Solved Examples

Example 1



From Sam's home, the route from home to the airport is marked in the map shown below. State whether the marking of the route forms a closed shape or not?

route in a map


Markings of the route do not form a closed shape.

It is an open shape as the sides do not meet at a point and left an opening in between.

\(\therefore\) The given shape is not a closed shape
Example 2



How many sides are there in the given shape? Is it a closed or open shape?

star shape


Count the number of straight lines in the star. There are 10 straight lines.

We can trace the outline of this star without any break. Hence, it is a closed shape.

It is a closed shape with 10 sides
Example 3



What is the least number of straight lines needed to form a closed shape?


In the case of curved lines, one curve is enough to form a closed shape. For example, a circle or an oval.

But, in the case of straight lines, at least 3 lines are needed to form a closed shape and in geometry, we call it a triangle.

Triangle is a closed shape

\(\therefore\) Minimum 3 lines are needed to form a closed shape

Now, try to solve the questions given from the open and closed shapes worksheet designed by our experts for your practice.

Interactive Questions on Closed Shapes

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.


Let's Summarize

We hope you enjoyed learning about closed shapes with the simulations and practice questions. Now, you will be able to easily solve problems on the definition of the closed shapes, closed shapes properties, and closed shapes examples.

About Cuemath

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.

Frequently Asked Questions (FAQs)

1. Is square a closed shape?

Yes, a square is a closed shape as all the sides of the square are connected.

2. Is a polygon a closed shape?

Yes, a polygon is a closed shape made up of straight lines.

3. What is a closed shape with 6 sides?

A closed shape with 6 sides is termed as a hexagon.