The Perimeter of Rectangle Formula and Applications
We come across many shapes whose distance around has to be calculated and this is termed as the perimeter of the shapes. We see many shapes around like square, rectangle, circle, polygon, etc. Every shape has its unique properties and measurements. Hence every shape has a different perimeter, based on their measurements. A perimeter is the length of the boundary enclosed by any geometric shape. The perimeter of the shape depends on the length of the shape. For example, a metal wire of length 10 cm can form both the circle and the square.
Suppose you have to fence your house, the length required for fencing is the perimeter of the house. Perimeters of two shapes can be equal only if their length is equal.
In this article, we will study what is a rectangle and perimeter of rectangle formula example.
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What is a Rectangle?
A rectangle is a quadrilateral having four sides. The opposite sides of a rectangle are parallel and of equal length. Since a rectangle has four sides, it has four angles.
All angles of a rectangle are equal. It is an equiangular rectangle with four right angles which is 90 degrees. Another property of the rectangle is that it has two diagonals of equal length. Diagonals are a line that is drawn inside the rectangle connecting opposite corners or vertices and hence the diagonals of a rectangle are congruent.
When we go round a closed figure or body, along its boundary, for once, we cover a distance. The measure of the distance is the perimeter of the figure or body. To understand and measure the perimeter of the rectangular field, we travel along the boundary of the four sides of the field, starting from a point and ending at the same point. While doing so, we observe that we measure the length and breadth, both, twice.
Some of the examples of rectangles are cement blocks, picture frames, posters, sheets of paper, the faces of play bricks that snap together, the sides of shoe boxes and cereal boxes, and a lot of other everyday objects.
Properties of a Rectangle
It is a flat shape.
It has 4 sides (edges).
It has 4 corners (vertices).
It has 4 right angles.
Perimeter of Rectangle
A four-sided polygon having two dimensions i.e. length and breadth are called a rectangle. The total distance covered by the boundaries or the sides in the case of the rectangle is known as the perimeter of a rectangle. To calculate the perimeter of the rectangle we have to add all four sides to the rectangle. In a rectangle, the total number of sides equals 4 therefore, its perimeter is defined as the sum of its four sides. The unit of a rectangle is represented in meters, centimetres, millimetres, inches, feet, square feet, and so on.
The Perimeter of Rectangle - Formula
The perimeter of a rectangle is the measure of the sum of its all sides which in the case of a rectangle are four sides in total. The perimeter, for any polygon, is defined as the total distance covered by its sides. Since the opposite sides in a rectangle have equal lengths and widths, the perimeter of the rectangle is twice the length of the rectangle plus twice the width of the rectangle.
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Perimeter of rectangle formula = sum of all the four sides
= length + width + length + width
= 2 length + 2 width
Perimeter of rectangle formula = 2 × (length + width)
Suppose a rectangle ABCD has length and width as a and b respectively.
We know that,
Perimeter of the rectangle P= 2(a+b) units
where the length of the rectangle is represented by a
the breadth of the rectangle is represented by b
The Perimeter of Rectangle - Derivation
The perimeter P of a rectangle is given by the sum of its all sides and since the sides that are opposite to each other are equal perimeter for a rectangle ABCD with length a and breadth b will be-
P= sum of its all sides
P= a+b+a+b
P= (a+b)
Hence Proved.
Area of Rectangle
Diagonals of a Rectangle
A rectangle has two diagonals, they are equal in length and intersect in the middle. A diagonal's length is the square root of (length2 + width2):
Diagonal 'd' = \[\sqrt{\left ( a^{2}+b^{2} \right )}\]
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Perimeter Formula Chart for Different Shapes
Here is the list of formulas for the perimeter of different shapes.
Formula of Perimeter of Different Shapes:
The Perimeter of Rectangle - Applications
The perimeter of a rectangle is very important in many everyday life activities and some of which are listed below-
The length of swimming races can be determined by using the perimeter of the rectangle if the swimming pool is constructed in a rectangular shape.
The length of the concrete boundary to be made before the construction of a house can be determined with the help of the perimeter.
The length of garden fences can be determined with the help of the perimeter formula.
The perimeter of the rectangle formula can be used in many art and crafts projects which required drawing borders of rectangular figures.
The Perimeter of Rectangle - Solved Example
Example 1:
Find the perimeter of a rectangle whose length and breadth are 11cm and 13cm, respectively.
Solution:
Given that length = 11 cm and Breadth = 13cm
We have,
The perimeter of rectangle formula = 2( length + breadth)
Perimeter, P = 2(11 + 13)
P = 2 x 24 cm
P = 56 cm
Therefore, the perimeter of a rectangle is 56 cm.
Example 2:
The length of the rectangular field is 15m and the width is 6m. Find the perimeter of a rectangle field and also find the area.
Solution:
Given that Length = 15m
Width = 6m
We have, Area formula A = length x width
= 15 x 6
= 90 m²
formula to calculate perimeter of rectangle P = 2 (length + width)
= 2 x (15 + 6)
= 2 x 21
= 42 m.
Example 3:
If the length and width of a rectangle are 12 cm and 15 cm respectively. Determine the perimeter.
Solution:
Given
Length= 12 cm
Width= 15 cm
We know that for a rectangle,
Perimeter= 2(length + width)
Perimeter= 2(12+15)
Perimeter= 2 x 27= 54 cm
Fun Facts
Many historical buildings are rectangular in shape e.g. Parthenon in Athens.
Conclusion
This is how we calculate the perimeter of a rectangle and apply it in different aspects. Understand how the perimeter of other closed figures is calculated and the formulas are derived.
FAQs on The Perimeter of Rectangle Formula
1. What is the Difference Between Area and Perimeter?
Key differences between area and perimeter are :
The area is the region occupied by the two-dimensional object. | Perimeter is the length of the boundary enclosed by the geometric figure. |
The area is the inner space of an object. | Perimeter is the length of the outer boundary of an object. |
The area represents a two-dimensional object so is measured in square units. | Perimeter represents a dimensional object so it is measured in linear units. |
Example: Space covered by a garden. | Example: Length of the boundary of the garden. |
2. Where do we use Perimeter in Daily Life?
Uses of the perimeter in daily life are as follows:
The perimeter of a plot is calculated for constructing buildings.
Perimeter is required for fencing the compound walls.
Perimeter is needed to sew edges of a quilt.
Perimeter is required to paste a decorative tape around the greeting card.
3. What is meant by the Area of the rectangle and its formula?
The area of any shape is the measure of the number of unit squares that can be fitted in that shape. Similarly, the area of the rectangle can be described as the total number of square units that can be fitted inside a rectangle, or in simple words, the area that is occupied by the rectangle within its boundary is referred to as the area of the rectangle. It is the product of its length and width and given by-
Area = (length x breadth) square units
4. What are some of the properties of the rectangle?
Some of the fundamental properties of a rectangle are listed below-
It is a quadrilateral.
It has four sides.
The opposite sides are equal and parallel.
The interior angles when added equal to 360°.
The diagonals bisect each other and there are a total of two diagonals.
The length of each diagonal is the same.
If the angle at which the diagonals bisect each other is 90°, then the rectangle is considered as a square.
5. What are some of the differences between a parallelogram and a rectangle?
The primary difference between a rectangle and a parallelogram is that the opposite sides are equal in the case of a parallelogram while the opposite sides are equal and the adjacent sides are perpendicular to each other in the case of a rectangle. Another key difference is that the diagonals are equal in the case of a rectangle while in the case of a parallelogram the lengths of the diagonals differ.
