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Shapes and Designs - 2D Shapes

Grade 3CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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2D shapes are flat figures that have only two dimensions - length and width. They have no thickness and look like drawings on a flat sheet of paper.

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A Square is a shape with 44 equal straight sides and 44 corners (vertices). You can visualize a square by looking at a standard dice face or a floor tile where all edges are exactly the same length.

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A Rectangle has 44 straight sides and 44 corners, where only the opposite sides are equal. Imagine a notebook or a chocolate bar; the long sides are equal to each other, and the short sides are equal to each other.

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A Triangle consists of 33 straight sides and 33 corners. It can look like a slice of pizza or a sandwich cut diagonally. The sides can be of different lengths or all the same.

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A Circle is a round shape with no straight sides and no corners. It has one continuous curved edge. Common examples include a 11-rupee coin, a bicycle wheel, or a wall clock.

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Edges in 2D shapes can be straight or curved. A square has 44 straight edges, while a circle has 11 curved edge. Some shapes, like a semi-circle, feature both one straight edge and one curved edge.

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Tiling (Tessellation) is the process of creating a pattern by repeating a shape over a flat surface without any gaps or overlaps. Think of a honeycomb made of hexagons or a brick wall where rectangles fit together perfectly.

📐Formulae

Number of sides in a triangle=3\text{Number of sides in a triangle} = 3

Number of corners in a square or rectangle=4\text{Number of corners in a square or rectangle} = 4

Total sides in nexttriangles=3×n\text{Total sides in } n ext{ triangles} = 3 \times n

Total sides in nextsquares=4×n\text{Total sides in } n ext{ squares} = 4 \times n

Number of corners in a circle=0\text{Number of corners in a circle} = 0

💡Examples

Problem 1:

Riya has 44 triangles and 33 squares. How many total corners (vertices) do all her shapes have together?

Solution:

  1. Number of corners in one triangle = 33.
  2. Total corners for 44 triangles = 4×3=124 \times 3 = 12.
  3. Number of corners in one square = 44.
  4. Total corners for 33 squares = 3×4=123 \times 4 = 12.
  5. Total corners = 12+12=2412 + 12 = 24.

Explanation:

To find the total number of corners, we multiply the number of each shape by its respective corners and then add the results together.

Problem 2:

If you place two identical squares side-by-side so that their edges touch perfectly, what is the name of the new shape formed and how many sides does it have?

Solution:

  1. When two squares are joined side-by-side, the resulting long shape is a Rectangle.
  2. A rectangle has 44 sides.

Explanation:

Joining two squares increases the length but not the number of sides of the outer boundary, transforming the equal-sided square into a rectangle with opposite sides equal.