Class 7 Maths Perimeter and Area Notes

Introduction:

The chapter “Perimeter and Area” in Class 7 Maths focuses on understanding how to calculate the perimeter and area of different geometric shapes. These concepts are essential for solving real-world problems related to measurements, construction, and design. The chapter explains how to calculate the perimeter and area of basic shapes like squares, rectangles, triangles, and circles. Students will also learn to apply these formulas in practical situations.

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Key Concepts Covered:

1. What is Perimeter?

• The perimeter of a figure is the total length of its boundary. It is calculated by adding up the lengths of all the sides of the figure.

Formulae:

• Square: $$P = 4 \times \text{side}$$P=4×side
• Rectangle: $$P = 2 \times (\text{length} + \text{breadth})$$P=2×(length+breadth)
• Triangle: $$P = \text{side 1} + \text{side 2} + \text{side 3}$$P=side 1+side 2+side 3
• Circle (Circumference): $$C = 2 \pi r$$C=2πr Where $r$r is the radius of the circle and $\pi \approx 3.14$π≈3.14.

Example:

• For a square with side length 5 cm: $$P = 4 \times 5 = 20 \, \text{cm}$$P=4×5=20cm

2. What is Area?

• The area of a figure is the amount of space enclosed within its boundary. It is measured in square units (e.g., cm², m²).

Formulae:

• Square: $$A = \text{side}^2$$A=side2
• Rectangle: $$A = \text{length} \times \text{breadth}$$A=length×breadth
• Triangle: $$A = \frac{1}{2} \times \text{base} \times \text{height}$$A=21​×base×height
• Circle: $$A = \pi r^2$$A=πr2 Where $r$r is the radius of the circle and $\pi \approx 3.14$π≈3.14.

Example:

• For a rectangle with length 6 cm and breadth 4 cm: $$A = 6 \times 4 = 24 \, \text{cm}^2$$A=6×4=24cm2

3. Perimeter and Area of Compound Figures:

• A compound figure is a figure made up of two or more simple shapes. To calculate the perimeter or area of compound figures, break the figure into simpler shapes (like rectangles, squares, or triangles), calculate the perimeter or area of each, and then add them together.

Example:
If a figure consists of a rectangle and a triangle, first calculate the area of the rectangle and triangle separately, and then add them to find the total area of the compound figure.

4. Word Problems Involving Perimeter and Area:

• In real-life situations, you often need to find the perimeter or area to solve practical problems, such as finding the amount of fencing required for a garden or the area of land for construction. For example:
  • If you want to paint a wall, you need to calculate the area of the wall.
  • If you are building a fence around a yard, you need to calculate the perimeter to know how much fencing material is required.

5. Units of Measurement:

• Perimeter is usually measured in linear units (such as cm, m, km, etc.).
• Area is measured in square units (such as cm², m², km², etc.).

Example:

• If the perimeter of a rectangular room is 30 meters, the unit of perimeter is meters (m).
• If the area of a rectangle is 50 square meters, the unit of area is square meters (m²).

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Important Questions with Answers:

1. What is the perimeter of a rectangle with length 8 cm and breadth 5 cm?
   • Answer: $$P = 2 \times (8 + 5) = 2 \times 13 = 26 \, \text{cm}$$P=2×(8+5)=2×13=26cm
2. What is the area of a square with side length 7 cm?
   • Answer: $$A = 7^2 = 49 \, \text{cm}^2$$A=72=49cm2
3. How do you calculate the area of a triangle with base 10 cm and height 6 cm?
   • Answer: $$A = \frac{1}{2} \times 10 \times 6 = 30 \, \text{cm}^2$$A=21​×10×6=30cm2
4. What is the perimeter of a triangle with sides 5 cm, 7 cm, and 8 cm?
   • Answer: $$P = 5 + 7 + 8 = 20 \, \text{cm}$$P=5+7+8=20cm
5. What is the area of a circle with radius 4 cm?
   • Answer: $$A = \pi \times 4^2 = 3.14 \times 16 = 50.24 \, \text{cm}^2$$A=π×42=3.14×16=50.24cm2
6. If the perimeter of a rectangle is 40 cm and the length is 12 cm, what is the breadth?
   • Answer:
     Using the formula for perimeter of a rectangle, $P = 2 \times (l + b)$P=2×(l+b): $$40 = 2 \times (12 + b) \quad \Rightarrow \quad 40 = 24 + 2b \quad \Rightarrow \quad 2b = 16 \quad \Rightarrow \quad b = 8 \, \text{cm}$$40=2×(12+b)⇒40=24+2b⇒2b=16⇒b=8cm