CBSE Class 6 Maths: Measurement & Mensuration Ex 10.1 - Perimeter

What is Perimeter?

Imagine you have a drawing of a square park. If you want to walk exactly along the edge of this park, the total distance you cover is its perimeter. In simple terms, Perimeter is the total length of the boundary of any closed flat shape. It's like measuring the 'outline' of something. We encounter perimeter in many daily activities, such as:

• Fencing: When a farmer wants to put a fence around their rectangular field, they need to know the perimeter to buy enough fencing material.
• Framing: To put a frame around a picture, you need to measure the perimeter of the picture to get the correct length of the frame.
• Lace work: If you want to add a lace border to a table cloth, you'd calculate the perimeter of the table cloth.

The unit of perimeter is the same as the unit of length, such as centimetres (cm), metres (m), or kilometres (km). For any shape, whether it's a simple square or an irregular polygon, finding its perimeter means adding up the lengths of all its sides. This fundamental concept helps us understand the size and boundaries of objects around us.

Key Definitions for Exercise 10.1

Perimeter

The total distance around the boundary of a closed two-dimensional shape. It is the sum of the lengths of all its sides.

Polygon

A closed shape made up entirely of straight line segments. Examples include triangles, squares, rectangles, pentagons, etc.

Regular Polygon

A polygon in which all sides are equal in length and all interior angles are equal. Examples include equilateral triangles and squares.

Calculating Perimeter for Different Shapes

1. Perimeter of a Rectangle — A rectangle has two pairs of equal sides: length (L) and width (W). To find its perimeter, you add all four sides: L + W + L + W. This simplifies to the formula: Perimeter = 2 × (Length + Width)
2. Perimeter of a Square — A square is a special type of rectangle where all four sides are equal in length. If 's' is the length of one side, then the perimeter is s + s + s + s. This simplifies to the formula: Perimeter = 4 × Side
3. Perimeter of a Triangle — A triangle has three sides. To find its perimeter, you simply add the lengths of all three sides. If the sides are 'a', 'b', and 'c', the formula is: Perimeter = a + b + c
4. Perimeter of an Irregular Polygon — For any closed shape made of straight lines (a polygon) where the sides might not all be equal, the rule remains the same: add the lengths of all its sides. There's no specific short formula, just sum up each side length.

Worked Examples: Finding Perimeter

• Example 1: Perimeter of a Rectangle A rectangular field is 15 meters long and 10 meters wide. Find its perimeter. Step 1: Identify the given dimensions. Length (L) = 15 m Width (W) = 10 m Step 2: Apply the formula for the perimeter of a rectangle. Perimeter = 2 × (Length + Width) Perimeter = 2 × (15 m + 10 m) Step 3: Calculate the sum and then multiply. Perimeter = 2 × (25 m) Perimeter = 50 m Final Answer: The perimeter of the rectangular field is 50 meters.
• Example 2: Perimeter of a Square Find the perimeter of a square photo frame with a side length of 20 centimetres. Step 1: Identify the given dimension. Side (s) = 20 cm Step 2: Apply the formula for the perimeter of a square. Perimeter = 4 × Side Perimeter = 4 × 20 cm Step 3: Calculate the product. Perimeter = 80 cm Final Answer: The perimeter of the square photo frame is 80 centimetres.
• Example 3: Perimeter of an Irregular Polygon An irregular polygon has sides measuring 4 cm, 6 cm, 3 cm, 7 cm, and 5 cm. What is its perimeter? Step 1: Identify the lengths of all sides. Sides: 4 cm, 6 cm, 3 cm, 7 cm, 5 cm Step 2: Add the lengths of all the sides. Perimeter = 4 cm + 6 cm + 3 cm + 7 cm + 5 cm Step 3: Calculate the sum. Perimeter = 25 cm Final Answer: The perimeter of the irregular polygon is 25 centimetres.

Exam Tip: Avoiding Common Mistakes in Perimeter Questions

When solving perimeter problems, especially in exams, students often make a few common errors. Be careful about these:

1. Forgetting Units: Always, always write the correct units (cm, m, km) with your final answer. A number without a unit is incomplete.
2. Confusing Perimeter with Area: Remember, perimeter is the distance around the shape (boundary), while area is the space inside the shape. Don't mix up the formulas or concepts.
3. Missing a Side in Irregular Polygons: When calculating the perimeter of an irregular polygon, ensure you add the length of every single side. It's easy to accidentally skip one side, especially if the diagram is complex. Count the sides and ensure each one is included in your sum.
4. Incorrect Formula Application: Double-check whether the shape is a square, rectangle, or triangle before applying its specific formula. For example, don't use 4 × side for a rectangle!

Practice Questions with Solutions

• Q: A rectangular garden is 30 m long and 18 m wide. What is the length of the wire needed to fence it once? A: Step 1: Identify the length (L) and width (W) of the garden. L = 30 m, W = 18 m. Step 2: Use the formula for the perimeter of a rectangle: Perimeter = 2 × (L + W). Perimeter = 2 × (30 m + 18 m) = 2 × (48 m). Step 3: Calculate the final perimeter. Perimeter = 96 m. Final answer: The length of the wire needed is 96 meters.
• Q: Find the perimeter of a square playground whose side is 25 meters. A: Step 1: Identify the side length (s) of the square playground. s = 25 m. Step 2: Use the formula for the perimeter of a square: Perimeter = 4 × s. Perimeter = 4 × 25 m. Step 3: Calculate the final perimeter. Perimeter = 100 m. Final answer: The perimeter of the square playground is 100 meters.
• Q: A triangle has sides measuring 8 cm, 10 cm, and 12 cm. What is its perimeter? A: Step 1: Identify the lengths of the three sides of the triangle. Sides = 8 cm, 10 cm, 12 cm. Step 2: Add the lengths of all three sides. Perimeter = 8 cm + 10 cm + 12 cm. Step 3: Calculate the sum. Perimeter = 30 cm. Final answer: The perimeter of the triangle is 30 centimetres.
• Q: A table top has sides measuring 1.5 m, 1 m, 1.5 m, and 1 m. Find the perimeter of the table top. A: Step 1: Identify the lengths of the four sides. Notice it's a rectangle. Side 1 = 1.5 m, Side 2 = 1 m, Side 3 = 1.5 m, Side 4 = 1 m. Step 2: Sum all the sides or use the rectangle formula. Perimeter = 1.5 m + 1 m + 1.5 m + 1 m = 5 m. Alternatively, L = 1.5 m, W = 1 m. Perimeter = 2 × (1.5 + 1) = 2 × 2.5 = 5 m. Step 3: State the final perimeter. Perimeter = 5 m. Final answer: The perimeter of the table top is 5 meters.

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