Maths Shapes and Patterns - CBSE Notes

What are Shapes?

Shapes help us understand the world around us. Everything we see has a shape—whether it's a ball, a book, or a pizza!

• Shapes are the outlines or boundaries of objects.
• They can be made using curves, points, and line segments.
• Some shapes have straight edges, while others are round.
• Examples: Circle, Square, Rectangle, Triangle.

Types of Shapes

1. Open Shapes

Some shapes do not have a complete boundary. They have gaps in between.

• Open shapes are made of line segments or curves that do not connect completely.
• Example: Letter C, Letter U, A curved line.
  

2. Closed Shapes

These shapes have a complete boundary with no gaps.

• A closed shape starts and ends at the same point.
• Example: Letter O, Letter B, Letter D, A triangle, A square.

Practice Question

Identify the open and the close shapes.

Answer: Figure 1 is open shape rest all figures are of close shape.

Common Shapes and Their Properties

1. Circle

A circle is a round shape that has no corners or straight lines.

• It is a two-dimensional (2D) shape.
• No edges, no corners.
• Examples: Steering wheel, Pizza, Dartboard.
  

2. Oval

An oval looks like a stretched circle.

• It has no straight lines or corners.
• Example: Number 0 (zero), An egg, A balloon.
  
  

3. Square

A square is a shape with four equal sides.

• All four sides are of the same length.
• It has four corners and four edges.
• Examples: Chessboard, Carrom board, Window pane.
  

4. Rectangle

A rectangle looks like a square but has two longer and two shorter sides.

• Opposite sides are equal in length.
• It has four corners and four edges.
• Examples: Laptop screen, Mobile phone screen, Door.

5. Triangle

A triangle has three sides and three corners.

• It can have different side lengths.
• Examples: Nachos, a slice of pizza, a road sign.
  
  

Counting Triangles

Triangles are often hidden inside bigger shapes. To count them, we follow a simple method:

• Step 1: Look at the shape carefully and find all the small triangles inside.
• Step 2: Number the base of each small triangle.
• Step 3: Add the numbers of the small triangles to find the total.

Let's Practise:

Sam wants to count the number of triangles present in the given image?

Ans: 
Here, Sam wants to count the total number of triangles present in theimage. So, Sam will use the concept of counting shapes to find how many triangles are present:
Step1: Identify the different shapes present in the image. Here, in theabove image, only triangles are present. 
Step2: Add the numbers to the base of the small triangles. Here, we have2 small triangles in the first layer and 2 small triangles in the second layer.

Step3: To calculate the total number of triangles, add base numbers present on each layer.

• Number of triangles in the first layer = 3
• Number of triangles in the second layer = 3
• Total number of triangles in both layers = 3+3 = 6
• So, the total number of triangles present in the image is 6

Parts of a Shape

1. Edges

Edges are the lines that make up a shape.

• Example: A square has 4 edges, a triangle has 3 edges.
  

2. Corners (Vertices)

Corners are the points where two edges meet.

• Example: A rectangle has 4 corners, a triangle has 3 corners.

Edges and Corners in Different Shapes

Patterns and Designs

Shapes can be used to create beautiful patterns.

• Patterns repeat the same shape again and again.
• We can find patterns in floor tiles, weaving, and nature.
• Examples of patterns:
  • Floor designs
  • Wall decorations
  • Tiling patterns

Practice Questions

1: Identifying Shapes

Look at the shapes below and answer the following questions:

Which of these shapes is an open shape?

(a) Triangle
(b) Letter C 
(c) Square
(d) Circle

View Answer  

Answer: (b) Letter C – It is an open shape because it does not have a closed boundary.

2. Which of these shapes has no edges and no corners?
(a) Rectangle
(b) Oval 
(c) Square
(d) Triangle

View Answer  

Answer: (b) Oval – It is a curved shape with no straight edges and no corners.

3. How many corners does a square have?
(a) 2
(b) 3
(c) 4
(d) 5

View Answer  Answer:
(c) 4 – A square has 4 corners.