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A rectangle is a form of quadrilateral with equal and parallel opposite sides. It’s a four-sided polygon with four 90-degree angles on each side The total length of each side of a rectangle is added together to determine the rectangle’s perimeter. As a direct consequence of this, we are able to compute the perimeter of a rectangle by adding together all four of its sides. The specified rectangle’s perimeter is a + b + a + b.
Perimeter of a Rectangle definition:
The term “perimeter” refers to the total distance that is covered by the four sides or edges of a rectangle. The total length of a rectangle’s four sides is added together to determine the rectangle’s perimeter. This is because a rectangle has four sides. Because the perimeter is a linear measurement, the unit of the rectangle’s perimeter will be metres, centimetres, inches, feet, and so on.
Perimeter of a Rectangle Formula:
The perimeter of a rectangle is equal to the sum of the rectangle’s sides. The perimeter formulas are the total distance around the sides of any polygon. In the case of a rectangle, the opposite sides are equal, hence the perimeter is equal to twice the width plus twice the length of the rectangle, and it is symbolised by the letter “p.” Let’s calculate its perimeter and area using the formula below.
P = 2 (a+b) units is the perimeter of a rectangle.
where
The rectangle’s length is denoted by “a.”
The width of the rectangle is denoted by “b.”
Derivation of Perimeter of Rectangle:
Because the perimeter is equal to the total of the polygon’s sides. As a consequence of this, the following constitutes the perimeter (P) of a rectangle;
P = total of all four sides
P = a + b + a + b (Opposite sides of rectangle are equal)
2(a + b) = P
As a result, derived.
Therefore,
A rectangle’s perimeter is equal to 2(Length + Width) square units.
Let us now construct the formula for the area of a rectangle in terms of the above-mentioned figure;
The area of a rectangle = Length × Width = a × b
Applications of Perimeter of Rectangle
The perimeter of a rectangle has several practical applications. Several of them are listed below for your convenience:
- Using the perimeter formula, we may calculate the length of a rectangular field or garden for fencing purposes.
- It can be used for a variety of art and craft projects, such as adding colourful ribbons or ropes to the border of rectangular cardboard.
- When building a rectangular swimming pool, the length of swimming races is dictated by the perimeter of the pool.
- For the house construction plan, we need to set a concrete border, which is doable using the perimeter calculation.
Examples using Perimeter of Rectangle Formula
Example 1: Calculate the perimeter of a rectangle with 12 cm and 8 cm sides.
Solution: Using the perimeter of rectangle formula, Perimeter of rectangle = 2(l + w), calculate the perimeter of the given rectangle. The rectangle’s length (l) and width (w) are stated as 12 cm and 8 cm, respectively.
We get Perimeter of rectangle = 2(l + w) = 2(12 + 8) = 2 x 20 = 40 cm by replacing the variables in the formula. As a result, the rectangle’s perimeter is 40 cm.
Example 2: What is the perimeter of a rectangle that is 15 metres long and 9 metres wide?
Solution: Length = 15 m; width = 9 m is given. We know that the formula for the perimeter of a rectangle is Perimeter of a rectangle = 2(l + w). P = 2(l + w) = 2(15 + 9) = 2 x 24 = 48 m is the result of substituting the supplied values. As a result, the supplied rectangle’s perimeter is 48 metres.
Area and Perimeter of a Rectangle Relationship:
Because the perimeter of a rectangle is the complete length of its boundary and is stated in linear units like cm, inches, and so on, there is no direct link between the area and perimeter of a rectangle. The formula for calculating the perimeter of a rectangle is 2(length + width). The area of a rectangle, on the other hand, is the total space filled by the rectangle and is measured in square units such as cm2, inches2, and so on. The area of a rectangle is calculated using the formula Area of rectangle = length x width.
Conclusion:
The perimeter of a rectangle simplifies things and aids us in our daily calculations of distances and lengths.
As an example,
- You may quickly calculate how much ribbon you’ll need to embellish the border of your rectangle notebook by finding the perimeter.
- If you need to erect a fence around your garden, measure the perimeter to determine the amount of wire you’ll need.
