Perimeter and Area

Notes on Perimeter and Area

6.1 Perimeter

Definition of Perimeter

• The perimeter of a closed plane figure is the total distance around the shape.
• For polygons, this is calculated by summing the lengths of all sides.

Perimeter Formulas

• Perimeter of a Rectangle:

  • For rectangle with length l and breadth b:
  • P = 2 × (l + b)
  • Example: Rectangle with l = 12 cm, b = 8 cm,
    • P = 2 × (12 cm + 8 cm) = 40 cm.

• Perimeter of a Square:

  • If side length is s, then:
  • P = 4 × s
  • Example: Square with side = 1 m:
    • P = 4 × 1 m = 4 m.

• Perimeter of a Triangle:

  • For a triangle with sides a, b, c:
  • P = a + b + c
  • Example: Triangle with sides 4 cm, 5 cm, and 7 cm:
    • P = 4 cm + 5 cm + 7 cm = 16 cm.

Practical Examples

• To find the length of lace needed around a tablecloth:
  • Length = 3 m, Breadth = 2 m; P = 2 × (3 m + 2 m) = 10 m.
• Calculate distance traveled: If a square park side = 75 m:
  • P = 4 × 75 m = 300 m, 3 rounds = 900 m.

6.2 Area

Definition of Area

• The area refers to the measure of the space enclosed within a closed figure.

Area Formulas

• Area of a Rectangle:

  • A = l × b
  • Example: For floor of length 5 m and width 4 m:
  • A = 5 m × 4 m = 20 sq m.

• Area of a Square:

  • A = s × s or A = s²
  • Example: For a carpet of side 3 m:
    • A = 3 m × 3 m = 9 sq m.

• The area of the remaining floor that is not carpeted:

  • Area not carpeted = Area of floor - Area of carpet = 20 sq m - 9 sq m = 11 sq m.

Area of Other Shapes

• Area of a Triangle:
  • Found using the formula: Area = 1/2 × base × height.
  • Deriving relationships between shapes can also show how areas relate.

Estimating Areas

• Areas can be roughly estimated using grid paper:
  • Each square counting as 1 square unit. Borders and overlapping issues are noted.

6.3 Applications

• Contextual problems and examples help in applying the concepts of perimeter and area in real-life situations.
• For instance, identifying land areas, carpet coverage, fencing fields, etc.

Conclusion

• Understanding perimeter and area is crucial as they apply to many real-world applications. The ability to calculate these efficiently is foundational in geometry.

1. Perimeter is the total distance around a shape, calculated by summing side lengths.
2. For a rectangle, Perimeter = 2 × (length + breadth).
3. For a square, Perimeter = 4 × side length.
4. For a triangle, Perimeter = sum of all three side lengths.
5. Area is the measure of space inside a shape, calculated using specific formulas based on the shape.
6. For a rectangle, Area = length × width; for a square, Area = side × side.
7. The area can be estimated using grid paper.
8. A figure can have the same area but different perimeters, or vice versa.
9. Understanding how to compute perimeter and area is essential for practical applications in everyday life.
10. Grid paper helps in visualizing and calculating areas and perimeters accurately.