Important Formulas: Perimeter and Area | Maths for Class 6 (Ganita Prakash) - New NCERT PDF Download

1. Perimeter: The perimeter of any closed shape is the total distance around its boundary.

2. Polygon Perimeter: For polygons, the perimeter is the sum of all the side lengths.

3. Perimeter of a Rectangle:

• Add the length and width.
• Multiply the sum by 2. 
• Perimeter = 2 (l+b)
  
• Example: A rectangle with a length of 12 cm and width of 8 cm has a perimeter of 40 cm.

4. Perimeter of a Square:

• The perimeter of a square = 4 x side. 
• Example: A square with a side length of 1 meter has a perimeter of 4 meters.

5. Perimeter of a Triangle:

• Sum the lengths of all three sides. P = a+ b+ c
• Example: A triangle with sides of 4 cm, 5 cm, and 7 cm has a perimeter of 16 cm.

• 6. Regular Polygon Perimeter:

  • Multiply the side length by the number of sides(n) .
    Perimeter = number of sides x length of side 
    P= n x s
  • Example: An equilateral triangle with side length 5 cm has a perimeter of 15 cm.
    

7. Area: Area is the amount of space inside a shape. The area is generally measured in square units.

8. Area of a Square: 

• Multiply the side by side. 
• Area = side x side = side²

9. Rectangle Area Calculation:

• Multiply the length by the width.  Area = L x W
• Example: A room 5 m by 4 m has an area of 20 square meters.

10. Triangle Area:

• The area of a triangle is half the area of a rectangle when cut diagonally.
• Area = 1/2 (base x height)
• Example: A rectangle cut into two triangles results in each triangle having half the rectangle’s area.

11. Two closed shapes can have the same area but different perimeters, or the same perimeter but different areas. 
To estimate or find the exact area of a region, you can break it into smaller squares or shapes like rectangles and triangles, whose areas can be calculated.