Plane Shapes

Have you noticed the shape of a pizza? It is round in shape.

Pizza is round in shape

If we cut out a slice from the pizza, the slice gets a triangular shape.

A slice of pizza in triangular in 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 two-dimensional 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 two-dimensional 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.

Plane Shape


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.

           

 
tips and tricks
Tips and Tricks
  • Count the number of sides to identify the shapes
  • Use paper cut-outs to visualize the shapes
  • Use everyday objects trace the surface and identify the plane shapes

What Are the Different 2D Shapes?

Polygon shapes images

Observe this sheet of paper.

A sheet of paper is 2 dimensional in shape

It consists of a length and a width.

A two-dimensional 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

A triangle is a 2D shape

Square 4

A square is a 2D shape

Rhombus 4

A rhombus is a 2D shape

Kite 4

A kite is a 2D shape

Rectangle 4

Rectangle is a 2D shape

Trapezium 4

A trapezium  is a 2D shape

Pentagon 5

A pentagon is a 2D shape

Hexagon 6

A hexagon is a 2D shape

Heptagon 7

A septagon 7 sided polygon

Octagon 8

An octagon is a 2D shape

Decagon 10

A decagon is a 10 sided polygon

Dodecagon 12

A dodecagon twelve sided polygon

Hexadecagon 16

A hexadecagon is a 16 sided polygon

Circle 0

A circle is a 2D shape


What Are Polygons?

Types of polygon

In geometry, a polygon is a closed two-dimensional 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.

honeycomb in a shape of polygon

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

Triangle
Trigon

4

Square
Tetragon

5

Pentagon
Pentagon

6

Hexagon
Hexagon

7

Heptagon
Heptagon

8

Octagon
Octagon

9

Nonagon
Nonagon

10

Deccagon
Decagon

11

Hendecagon
Hendecagon

12

Dodecagon
Dodecagon

13

13 sided polygon
Tridecagon

14

14 sided polygon
Tetradecagon

15

15 sided polygon
Pentadecagon

16

16 sided polygon
Hexadecagon

17

17 Sided polygon
Heptadecagon

18

18 sided polygon
Octadecagon

19

19 sided polygon

Enneadecagon

20

20 sided polygon

Icosagon

What Are the Properties of Shapes?

The properties of different shapes are as follows:

2D shape Property

Properties of quadrilaterals: Properties of a square

Square

A square is a quadrilateral with four equal sides and four right angles.

Properties of quadrilaterals: Properties of a rectangle

Rectangle

A rectangle is a quadrilateral with two pairs of equal and parallel opposite sides and four right angles.

 

Circle - center and radius

Circle

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. 

A triangle PQR

Triangle

A triangle is a closed figure or shape with 3 sides, 3 angles, and 3 vertices.

polygns with sides

Polygon

A polygon is a closed two-dimensional figure with three or more straight lines.

oval shape

Oval

Oval has no straight line, or corner, or side to it. It is a closed shape made of curved lines.
 
important notes to remember
Important Notes
  1. Polygons are 2-D figures with more than 3 sides.
  2. Angles of a polygon can be measure by using the following formulas:
    Exterior Angle = \(\dfrac{360^\circ}{n}\)
    Interior angle = \(\dfrac{180^\circ (n-2)}{n}\)
    Here n refers to the number of sides.

Solved Examples

Example 1

 

 

Help Ruth figure out the polygon shape in the hanger.

Triangle shaped hanger

Solution

The hanger looks like a trigon or a three-sided 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?

Number of sides in a star 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.

Not a hexagon

Solution

A hexagon has 6 sides.

So Anna should pick the polygon with only 6 sides.

The 6-sided polygons are:

Types of polygons

\(\therefore\) Anna picked all the hexagon polygons.
Example 4

 

 

Does the given figure have a two-dimensional shape? How many sides does it have?

Shape of a football is spherical

Solution

The football looks like a sphere and has 0 sides.

No, football does not have a two-dimensional shape.

The figure does not have a two-dimensional 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.

 

 
 
 
 
 
 
Challenge your math skills
Challenging Questions
  1. Is a circle a polygon?
  2. Is the given shape a quadrilateral? 
  3. A shape that is not a quadrilateral

Let's Summarize

The mini-lesson 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 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.


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.

  
More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus
More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus