Perimeter and Area Class 7 Worksheet: Master Key Concepts Easily

Understanding Perimeter: Definition and Formulae

The perimeter of a shape is the total distance around its boundary. It is measured in units like cm, m, or mm.

Key points:

• Perimeter applies to all 2D shapes.
• Add the lengths of all sides to find perimeter.

Examples:

• Square: $P = 4 \times \text{side}$
• Rectangle: $P = 2 \times (\text{length} + \text{breadth})$

Knowing perimeter helps in real-life tasks like fencing a garden or framing a picture.

Exploring Area: What It Means and How to Calculate

Area is the amount of surface a shape covers. It is measured in square units such as $\text{cm}^2$, $\text{m}^2$.

Important formulas:

• Square: $A = \text{side}^2$
• Rectangle: $A = \text{length} \times \text{breadth}$

Area helps in tasks like painting walls or laying tiles.

Worked example: Find the area of a rectangle with length 8 cm and breadth 5 cm.

$$ A = 8 \times 5 = 40 \text{ cm}^2 $$

Difference Between Perimeter and Area: A Quick Comparison

Understanding how perimeter and area differ is crucial:

This helps avoid confusion in solving problems.

Perimeter and Area of Common Shapes in Class 7 NCERT

Besides squares and rectangles, Class 7 NCERT covers:

• Triangle:
• Perimeter = sum of all sides
• Area = $\frac{1}{2} \times \text{base} \times \text{height}$

• Parallelogram:
• Perimeter = $2 \times (\text{base} + \text{side})$
• Area = $\text{base} \times \text{height}$

• Circle:
• Circumference (perimeter) = $2 \pi r$
• Area = $\pi r^2$

Practice these formulas with examples to score well.

Tips to Solve Perimeter and Area Problems in Class 7

Follow these steps for accuracy:

• Read the problem carefully.
• Identify the shape and dimensions.
• Choose the correct formula.
• Substitute values and calculate.
• Double-check units and answers.

Use diagrams to visualize the problem. Practice with NCERT exercises and worksheets regularly.

Sample Perimeter and Area Class 7 Worksheet Questions

Try these questions to test your understanding:

1. Find the perimeter of a square with side 7 cm. 2. Calculate the area of a rectangle with length 12 cm and breadth 9 cm. 3. A triangle has sides 5 cm, 6 cm, and 7 cm. Find its perimeter. 4. Find the area of a circle with radius 4 cm (use $\pi = 3.14$).

Solutions:

1. $P = 4 \times 7 = 28$ cm 2. $A = 12 \times 9 = 108$ $\text{cm}^2$ 3. $P = 5 + 6 + 7 = 18$ cm 4. $A = 3.14 \times 4^2 = 3.14 \times 16 = 50.24$ $\text{cm}^2$