What is Comparing Perimeters?

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Grade Level:

Class 2

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Definition

What is it?

Comparing perimeters means finding out which closed shape has a longer or shorter boundary. It helps us understand the size of the 'outline' of different objects. We do this by calculating the perimeter of each shape and then comparing the numbers.

Simple Example

Quick Example

Imagine you have two cricket grounds, one rectangular and one square. To know which ground has a longer boundary for the fence, you would compare their perimeters. If the rectangular ground needs 400 meters of fence and the square ground needs 380 meters, the rectangular ground has a longer perimeter.

Worked Example

Step-by-Step

Let's compare the perimeter of a square photo frame and a rectangular painting.

Step 1: Find the perimeter of the square photo frame. Each side of the square frame is 10 cm. Perimeter of square = 4 x side = 4 x 10 cm = 40 cm.
---Step 2: Find the perimeter of the rectangular painting. The length of the painting is 12 cm and the width is 8 cm. Perimeter of rectangle = 2 x (length + width) = 2 x (12 cm + 8 cm) = 2 x 20 cm = 40 cm.
---Step 3: Compare the perimeters. The square frame's perimeter is 40 cm. The rectangular painting's perimeter is 40 cm.
---Step 4: Conclude the comparison. Both the square photo frame and the rectangular painting have the same perimeter.

Answer: Both shapes have a perimeter of 40 cm, so they are equal.

Why It Matters

Comparing perimeters is crucial in fields like architecture for designing buildings, in sports for marking playing fields, and in fashion for cutting fabric. Engineers use it to calculate materials needed, and city planners use it for fencing parks. It's a basic skill that helps in many real-world jobs, from construction to design.

Common Mistakes

MISTAKE: Students sometimes compare areas instead of perimeters. | CORRECTION: Remember, perimeter is the distance around the edge, like a fence. Area is the space inside, like a carpet.

MISTAKE: For rectangles, students might only add length + width. | CORRECTION: The perimeter of a rectangle is 2 x (length + width) because there are two lengths and two widths.

MISTAKE: Not using the correct units when stating the perimeter. | CORRECTION: Always write the unit (like cm, m, km) after the number, for example, '25 cm' not just '25'.

Practice Questions

Try It Yourself

QUESTION: A square park has a side of 50 meters. A rectangular garden has a length of 60 meters and a width of 40 meters. Which has a longer perimeter? | ANSWER: Perimeter of square park = 4 x 50 = 200 m. Perimeter of rectangular garden = 2 x (60 + 40) = 2 x 100 = 200 m. Both have the same perimeter.

QUESTION: A triangular flag has sides of 30 cm, 40 cm, and 50 cm. A square handkerchief has a side of 35 cm. Which one has a shorter perimeter? | ANSWER: Perimeter of triangular flag = 30 + 40 + 50 = 120 cm. Perimeter of square handkerchief = 4 x 35 = 140 cm. The triangular flag has a shorter perimeter.

QUESTION: A farmer wants to fence two fields. Field A is a rectangle with length 75m and width 45m. Field B is a square with a side of 60m. If fencing costs Rs 100 per meter, which field will cost more to fence and by how much? | ANSWER: Perimeter of Field A = 2 x (75 + 45) = 2 x 120 = 240 m. Cost for Field A = 240 x 100 = Rs 24,000. Perimeter of Field B = 4 x 60 = 240 m. Cost for Field B = 240 x 100 = Rs 24,000. Both fields will cost the same to fence.

MCQ

Quick Quiz

Which of these statements is true when comparing the perimeters of two shapes?

The shape with more sides always has a longer perimeter.

The shape that looks bigger always has a longer perimeter.

You must calculate the perimeter of each shape and then compare the numerical values.

Comparing perimeters is the same as comparing areas.

The Correct Answer Is:

To compare perimeters accurately, you need to calculate the total length of the boundary for each shape and then compare those numbers. Looking at the shape or counting sides can be misleading.

Real World Connection

In the Real World

When a tailor stitches clothes, they need to compare the perimeter of different fabric pieces to make sure they fit together correctly. For example, comparing the perimeter of a sleeve opening to the perimeter of the main shirt body ensures a perfect fit. Similarly, when building a house, masons compare perimeters of walls to order the correct length of skirting tiles.

Key Vocabulary

Key Terms

PERIMETER: The total distance around the edge of a closed shape. | COMPARE: To find out if one thing is bigger, smaller, or the same as another. | RECTANGLE: A four-sided shape with two pairs of equal sides and four right angles. | SQUARE: A four-sided shape with all sides equal and four right angles. | LENGTH: The longest side of a rectangle.

What's Next

What to Learn Next

Now that you understand comparing perimeters, you can move on to 'Comparing Areas'. Area helps us understand the space inside a shape, which is another important way to compare objects. It builds on your understanding of shapes and measurements.