2D – Shapes – Definition – Properties 

Here is a detailed explanation of common 2D shapes, including their definitions, examples, diagrams, and properties:

Definition:

2D shapes are flat and also known as plane shapes, ‘2D’ stands for 2-dimensional. These shapes can be drawn on paper and have length and width. We can measure length and width.

Example: Rectangle, triangle, square, circle, oval, etc. are 2 dimensional objects.

1. Circle

Definition: A circle is a shape with all points the same distance from its center.

Example: Coins, plates, and wheels.

Diagram:

Properties:

• All points on the circle are equidistant from the center.
• The distance from the center to any point on the circle is called the radius.
• The longest distance across the circle (through the center) is called the diameter (d = 2r).
• The circumference (perimeter) is given by C = 2πr.
• The area is given by A = πr².

2. Square

Definition: A square is a quadrilateral with all four sides of equal length and all four angles equal to 90 degrees.

Example: Chessboard squares, tiles, and crackers.

Diagram:

Properties:

• Sides: All four sides are equal in length.
• Angles: All four angles are right angles (90 degrees).
• Perimeter (P): The total length around the square.
• P = 4s (where sss is the length of a side).
• Area (A): The space enclosed by the square. A = s².

3. Rectangle

Definition: A rectangle is a quadrilateral with opposite sides equal in length and all four angles equal to 90 degrees.

Example: Books, doors, and screens.

Diagram:

Properties:

• Sides: Opposite sides are equal in length.
• Angles: All four angles are right angles (90 degrees).
• Perimeter (P): The total length around the rectangle. P = 2l + 2w (where l is the length and w is the width).
• Area (A): The space enclosed by the rectangle. A = lw.

4. Triangle

Definition: A triangle is a polygon with three edges and three vertices.

Example: Traffic signs, pyramids (base), and slice of pizza.

Diagram:

Properties:

• Types by Sides:
  • Equilateral: All three sides are equal.
  • Isosceles: Two sides are equal.
  • Scalene: All three sides are different.
• Types by Angles:
  • Acute: All angles are less than 90 degrees.
  • Right: One angle is exactly 90 degrees.
  • Obtuse: One angle is more than 90 degrees.
• Perimeter (P): The total length around the triangle. P = a + b + c (where a, b, and c are the lengths of the sides).
• Area (A): The space enclosed by the triangle. A = 1/2 × base × height.

5. Parallelogram

Definition: A parallelogram is a quadrilateral with opposite sides parallel and equal in length.

Example: Rhombus, diamond shapes, and certain desk tops.

Diagram:

Properties:

• Sides: Opposite sides are equal and parallel.
• Angles: Opposite angles are equal. Adjacent angles add up to 180 degrees.
• Perimeter (P): The total length around the parallelogram. P = 2a + 2b (where a and b are the lengths of the sides).
• Area (A): The space enclosed by the parallelogram. A = base × height.

6. Rhombus

Definition: A rhombus is a quadrilateral with all four sides of equal length and opposite sides parallel.

Example: Kite shapes, diamond-shaped road signs.

Diagram:

Properties:

• Sides: All four sides are equal in length.
• Angles: Opposite angles are equal. Adjacent angles add up to 180 degrees.
• Perimeter (P): The total length around the rhombus. P = 4s (where s is the length of a side).
• Area (A): The space enclosed by the rhombus. A = 1/2 × d₁ × d₂ (where d₁ and d₂ are the lengths of the diagonals).

7. Trapezoid (Trapezium in UK)

Definition: A trapezoid is a quadrilateral with at least one pair of parallel sides.

Example: Trapezoidal roof, handbags, and certain tables.

Diagram:

Properties:

• Sides: One pair of opposite sides are parallel (called bases), and the other pair are non-parallel (called legs).
• Angles: The angles on the same side of a leg are supplementary (add up to 180 degrees).
• Perimeter (P): The total length around the trapezoid. P = a + b + c + d (where a, b, c, and d are the lengths of the sides).
• Area (A): The space enclosed by the trapezoid. A = 1/2​ × (b₂ ​+ b₂​) × h (where b₁​ and b₂ are the lengths of the parallel sides, and h is the height).

These diagrams and explanations should help in understanding the basic properties of common 2D shapes.