Perimeter of Rectangles

In geometry, understanding how to calculate the perimeter of shapes is an essential skill. Today, we're going to focus on finding the perimeter of rectangles. A rectangle is a four-sided polygon whose opposite sides are equal in length. The opposite sides are parallel, making it a type of parallelogram.

What is the perimeter?

The perimeter of a shape is the total length around that shape. It's like imagining a fence that surrounds a garden: the fence has a length, and if you walk around the fence, you'll measure the perimeter.

Understanding the rectangle

A rectangle has four sides: two lengths (the longer sides) and two widths (the shorter sides). Here's a simple representation:

Formula for perimeter of rectangle

To find the perimeter of a rectangle, you need to add up the lengths of all the sides. Since the opposite sides of a rectangle are equal, you only need to calculate:

Perimeter = 2 × (length + breadth)

Let's break down this formula:

• Length is the longer side of the rectangle.
• Width is the smaller side of the rectangle.
• Multiply the sum of the length and width by 2, because the length and width are two each.

Simple example

Perimeter = 2 × (length + breadth)
          = 2 × (8 + 3)
          = 2 × 11
          = 22 units
    

Why is it important to find the perimeter?

Perimeter calculations are useful in many real-life contexts, such as determining how much fencing is needed for a yard, the length of trim for a room, or even the length of the border around a painting.

Exercises for practice

Let's practice finding the perimeter of a rectangle. Suppose we have a rectangle whose area is:

• Length = 10 units
• Width = 5 units

Use of the formula:

Perimeter = 2 × (length + breadth)
          = 2 × (10 + 5)
          = 2 × 15
          = 30 units

Therefore, the perimeter is 30 units. Try practicing this with different rectangles by varying the length and width.

Advanced example

Let's challenge ourselves with a larger rectangle. Suppose you have a rectangle where:

• Length = 25 units
• Width = 10 units

Calculating the Perimeter:

Perimeter = 2 × (length + breadth)
          = 2 × (25 + 10)
          = 2 × 35
          = 70 units

The perimeter of this rectangle is 70 units.

Imagining different scenarios

Let us look at various verses to make this concept more concrete:

Perimeter = 2 × (length + breadth)
          = 2 × (6 + 4)
          = 2 × 10
          = 20 units
    

Perimeter = 2 × (length + breadth)
          = 2 × (9 + 3)
          = 2 × 12
          = 24 units
    

Compare perimeter

By calculating the perimeter of different rectangles, you can compare how length and width affect the total perimeter. Consider two rectangles:

Perimeter = 2 × (length + breadth)
          = 2 × (15 + 5)
          = 2 × 20
          = 40 units
    

Perimeter = 2 × (length + breadth)
          = 2 × (10 + 10)
          = 2 × 20
          = 40 units
    

Even though the dimensions are different, rectangles A and B both have a perimeter of 40 units. This shows how different lengths and widths can still lead to the same perimeter.

Summary and further practice

Understanding the perimeter of rectangles helps with real-world applications and builds basic geometry skills. Practice with different lengths and widths to gain confidence in using the formula:

Perimeter = 2 × (length + breadth)

Use different numbers for length and width and calculate the perimeter each time. This repeated practice will strengthen your knowledge and prepare you for more complex geometric concepts.

This introduction to the perimeter of rectangles establishes a fundamental understanding for further study in geometry, shapes, and mathematical problems related to measurement and dimensions.

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