Have you noticed the shape of a pizza? It is round in shape.
If we cut out a slice from the pizza, the slice gets a triangular shape.
In this lesson, you will learn all about plane shapes, types of plane shapes, and geometric shapes. You can check out the interactive simulations to know more about the lesson and try your hand at solving a few interesting practice questions at the end of the page. So, what are you waiting for?
Let's begin!
Lesson Plan
What Are Plane Shapes?
A plane shape is a twodimensional closed figure that has no thickness.
A plane in geometry is a flat surface that extends into infinity in all directions.
A plane has no thickness. It is also known as a twodimensional surface.
It has infinite width and length, zero thickness, and zero curvature.
It is actually difficult to imagine a plane in real life, there is nothing that we can use as a real example of a geometric plane.
We can see an example of a plane in coordinate geometry where the position of any given point on a plane is defined with the help of an ordered pair of numbers, or coordinates. Coordinates show the correct location of points in the plane.
What Are Open and Closed Shapes?
A closed figure can be made of straight or curved lines. It has no opening. Given below is an example of a closed figure.
An open figure is made of either straight or curved lines. However, it has at least one opening. Given below is an example of an open figure.
Sides and Corners
We have learned what plane shapes are and what they look like. Plane shapes are two dimensional, e.g., squares, triangles, and circles. The straight lines that make up a plane shape are called sides. The points where two sides meet are called corners.
 Count the number of sides to identify the shapes
 Use paper cutouts to visualize the shapes
 Use everyday objects trace the surface and identify the plane shapes
What Are the Different 2D Shapes?
Observe this sheet of paper.
It consists of a length and a width.
A twodimensional shape does not have any depth.
2D shapes are closed shapes that are created by joining straight/curved lines together.
Explore different polygons below changing with the number of sides.
The common 2D shapes are:
\(2\text{D}\) Shapes Name  Number of sides  Image 
Triangle  3  
Square  4  
Rhombus  4  
Kite  4  
Rectangle  4  
Trapezium  4  
Pentagon  5  
Hexagon  6  
Heptagon  7  
Octagon  8  
Decagon  10  
Dodecagon  12  
Hexadecagon  16  
Circle  0 
What Are Polygons?
In geometry, a polygon is a closed twodimensional figure with three or more straight lines.
The Greek word ‘Polygon’ consists of Poly meaning ‘many’ and gon meaning ‘angle.’
We see many different polygons around us.
For example, Have you ever seen a honeycomb? Can you guess ideally, how many sides a honeycomb could have?
A honeycomb is hexagonal in shape. You can very well relate the shape of a 6 sided polygon with a honeycomb.
The types of polygons are categorized into three major forms:
Let us look at a few different types of polygons with their sides:
Sides 
Shape and Name of A Polygon 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 
Enneadecagon 
20 
Icosagon 
What Are the Properties of Shapes?
The properties of different shapes are as follows:
2D shape  Property 

Square 
A square is a quadrilateral with four equal sides and four right angles. 
Rectangle 
A rectangle is a quadrilateral with two pairs of equal and parallel opposite sides and four right angles. 
Circle 
A circle is formed by the set of points which are at a constant or fixed distance (radius) from a fixed point (center) in the plane. 
Triangle 
A triangle is a closed figure or shape with 3 sides, 3 angles, and 3 vertices. 
Polygon 
A polygon is a closed twodimensional figure with three or more straight lines. 
Oval 
Oval has no straight line, or corner, or side to it. It is a closed shape made of curved lines. 
 Polygons are 2D figures with more than 3 sides.

Angles of a polygon can be measure by using the following formulas:
Exterior Angle = \(\dfrac{360^\circ}{n}\)
Interior angle = \(\dfrac{180^\circ (n2)}{n}\)
Here n refers to the number of sides.
Solved Examples
Example 1 
Help Ruth figure out the polygon shape in the hanger.
Solution
The hanger looks like a trigon or a threesided polygon because it has three sides.
\(\therefore\) The hanger resembles a trigon. 
Example 2 
How many sides are there in the given shape? Is it a closed or an open shape?
Solution
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 
Anna needs help in picking the only hexagon polygons.
Solution
A hexagon has 6 sides.
So Anna should pick the polygon with only 6 sides.
The 6sided polygons are:
\(\therefore\) Anna picked all the hexagon polygons. 
Example 4 
Does the given figure have a twodimensional shape? How many sides does it have?
Solution
The football looks like a sphere and has 0 sides.
No, football does not have a twodimensional shape.
The figure does not have a twodimensional shape. 
Interactive Questions
Here are a few activities for you to practice.
Select/type your answer and click the "Check Answer" button to see the result.
 Is a circle a polygon?
 Is the given shape a quadrilateral?
Let's Summarize
The minilesson targeted the fascinating concept of plane shapes. The math journey around plane shapes started with what a student already knew and went on to creatively crafting a fresh concept in the young minds. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever.
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 learningteachinglearning 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.
FAQs on Plane Shapes
1. Is a circle a polygon?
A polygon is a closed shape formed by straight lines.
A circle is a round shape formed by curved lines.
Therefore, a circle is not a polygon.
2. What is the difference between 2D and 3D shapes?
A 2D shape has two dimensions whereas a 3D shape has three dimensions  length, width, and height.
3. When depth is added to a 2D shape it becomes?
When depth is added to a 2D shape with length and width, it becomes a 3D shape.
4. How many triangles are there in a pentagon?
The number of triangles is 35 in a pentagon when all diagonals are formed.