Perimeter of Rectangle

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

The perimeter of a rectangle is the total length or distance of its boundary on all sides. The perimeter of a rectangle is a linear measure and is expressed in linear units of meters, feet, inches, or yards. Let us first understand the two main properties of a rectangle.

• All four angles of a rectangle are 90°.
• The opposite sides of a rectangle are equal in measure.

Imagine a rectangular park in your neighborhood. Have you ever thought about how long its boundary is?

If you go around the park along its boundary once, you cover a distance. This distance is the perimeter of the park. In order to measure the perimeter of any rectangular field, you travel along the boundary of the four sides of the field. You begin at a fixed point called the starting point and end when you reach the starting point again. This length or distance of the boundary is called the perimeter of a rectangle.

The formula used to calculate the perimeter of a rectangle is, perimeter of a rectangle = 2(l + w), where 'l' is the length and 'w' is the width of the rectangle. Let us understand this with the help of a simple example. David wants to put a fence around his farm so that his sheep does not wander away. Let us now understand this formula with an example. He wants to know how much wire he would need to put a fence around his rectangular farm.

Let us first name the sides of his farm. The larger side of this rectangular farm is named (l). The smaller side is named (w). Now, if we add the distance of all 4 sides of his farm, it will give us the perimeter. Total distance = l + w + l + w = 2l + 2w. Therefore, the Perimeter of a rectangle = 2(l + w). Let us use this formula in the following examples.

Examples using Perimeter of Rectangle Formula

Example 1: Find the perimeter of a rectangle whose sides are 12 cm and 8 cm.

Solution: Let us find the perimeter of the given rectangle using the perimeter of rectangle formula, Perimeter of rectangle = 2(l + w). It is given that the length (l) of the rectangle = 12 cm, and width (w) = 8 cm

On substituting the values in the formula, we get, Perimeter of rectangle = 2(l + w) = 2(12 + 8) = 2 × 20 = 40 cm. Therefore, the perimeter of the rectangle is 40 cm.

Example 2: What is the perimeter of a rectangle with a length of 15 m and a breadth of 9 m?

Solution: Given, Length = 15 m; Breadth (width) = 9 m. We know that the Perimeter of rectangle formula is expressed as, Perimeter of a rectangle = 2(l + w). Let us substitute the given values which means, P = 2(l + w) = 2(15 + 9) = 2 × 24 = 48 m. Therefore, the perimeter of the given rectangle is 48 m.

Perimeter of Rectangle Formula vs Perimeter of Square Formula

The perimeter of a rectangle formula is different from the formula for the perimeter of a square.

• The perimeter of rectangle formula is expressed as Perimeter of rectangle = 2(l + w); where 'l' is the length and 'w' is the width. However, the perimeter of a square formula is expressed as, perimeter of a square = 4 × s; where 's' is the side length.
• The perimeter of rectangle formula is different from the perimeter of a square because only the opposite sides of a rectangle are equal. However, in case of a square, all the sides are of equal length.

Relationship Between Area and Perimeter of a Rectangle

There is no direct relationship between the area and perimeter of rectangle because the perimeter of a rectangle is the total length of its boundary and is expressed in linear units like cm, inches, and so on. The perimeter of a rectangle formula = 2(length + width). On the other hand, the area of a rectangle is the total space occupied by the rectangle and is expressed in square units like, cm², inches², and so on. The formula for the area of a rectangle is, Area of rectangle = length × width

We can calculate the perimeter of a rectangle in three simple steps. The three steps listed below are helpful to find the perimeter.

• Step 1: To calculate the perimeter of a rectangle, the length and width should be known.
• Step 2: The respective values of length and width are substituted in the formula.
• Step 3: After solving the equation, the value of the perimeter is calculated.

We know that the formula used to calculate the perimeter of a rectangle is:

Perimeter of a rectangle = 2(l + w); where 'l' is the length and 'w' is the width of the rectangle.

There are other scenarios where the perimeter of a rectangle is known and the other dimensions are missing. In that case, we use the following formulas:

• If the perimeter and the length of a rectangle are known, the width can be calculated using the formula: Width = P/2 - l, where l = length of the rectangle; and w = width of the rectangle, and P = perimeter of the rectangle.
• In the same way, if the perimeter and the width are known, the length can be calculated using the formula: Length(L) = P/2 - w. Where P = perimeter of the rectangle; and w = width of the rectangle.

The perimeter of a rectangle makes things easier and helps us in calculating distances and lengths in our day-to-day lives.

For example,

• If you need to decorate the border of your rectangular notebook, you can easily calculate how much ribbon you would need by finding the perimeter.
• If you need to put a fence around your garden, the perimeter of the garden will give you the exact length of wire you would need.

Can you think of other similar examples related to the perimeter of a rectangle?

Try Cuemath's 'Perimeter of a rectangle Calculator', an online tool that calculates the perimeter of a rectangle. It is the easiest and the fastest method to calculate the answers promptly in seconds.

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• Area and Perimeter Of Rectangles Worksheets
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What is Perimeter of Rectangle in Math?

The perimeter of a rectangle in math is defined as the total length or distance around the boundary of a rectangle. The perimeter of a rectangle is measured in linear units like meters, feet, inches, yards, and so on.

What is the Perimeter of a Rectangle Formula?

The basic formula that is used to calculate the perimeter of a rectangle is: Perimeter of a rectangle = 2(l + w); where 'l' is the length of the rectangle and 'w' is the width of the rectangle. Apart from this, there are other formulas that are used to solve questions in which the perimeter is given but the other dimensions are not known. A few of them are given below:

• If the perimeter and the length of a rectangle are known, the width (w) = P/2 - l, where l = length, w = width, and P = perimeter of the rectangle.
• If the perimeter and the width are known, Length(L) = P/2 - w. Where P = perimeter of the rectangle; and w = width.

☛ Check all the other important math formulas in the following links:

• Perimeter Formula
• Measurement Formula
• Geometry Formulas

How to Find the Area of a Rectangle in Terms of Perimeter of a Rectangle?

If the perimeter of a rectangle is given, we also need to know either the length or the width to find its area. For example, if the length and perimeter is given, the width can be calculated. Perimeter = 2(length + width), width = (Perimeter/2) - length. Now, the required values to find the area of a rectangle are known. So, these values can be substituted in the formula: Area = length × width, and the area of the rectangle can be calculated.

How to Find the Perimeter of Rectangle with Diagonal?

The perimeter of a rectangle can be calculated if its diagonal and one side length is given. Since the diagonal of a rectangle forms a right-angled triangle in the rectangle, we use the Pythagoras theorem to derive the formula for the perimeter of a rectangle using the diagonal. Perimeter of rectangle with diagonal = 2l + 2 √(d² - l²); where 'l' is the length of the rectangle and 'd' is the length of the diagonal.

How to Find the Perimeter of a Rectangle?

The perimeter of a rectangle is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width). It is the measure of the total boundary of the rectangle and is expressed in linear units like cm, inches, yards, and so on.

What are the Units of Perimeter of a Rectangle?

The perimeter of a rectangle is measured in linear units, like meters, centimeters, inches, or yards. The perimeter is equal to the boundary of the rectangle which can be calculated with the formula: Perimeter = Length + Length + Width + Width = 2(Length + Width).

Is the Area and Perimeter of Rectangle the Same?

No, the area and the perimeter of a rectangle are different. The area of a rectangle is the total space covered by it and it is expressed in square units, while the perimeter is the total measure of its boundary and it is expressed in linear units.

How to Find the Perimeter of a Rectangle with Area?

If the area of a rectangle is given, we need to know either the length or the width of the rectangle to find its perimeter. For example, if the length and the area is known, the width can be calculated: Area = length × width. So, width = Area /length. Now, all the required values to calculate the perimeter of a rectangle are known. So, these values can be substituted in the formula: Perimeter = 2(length + width).