Perimeter & Area of Rectangle: Formula and Definition

Perimeter and Area of Rectangle: A rectangle is a parallelogram with four right angles. In general, a rectangle is also a parallelogram, but not all parallelograms are rectangles. The perimeter of a rectangle is the length of all sides of a closed figure. The length of all the sides will determine the perimeter of a rectangle. In Math’s, we are studying a variety of geometric shapes, like a square, rectangle, triangle, circle, etc. These shapes are compared on the basis of the perimeter, area, and other properties, so a thorough understanding of these properties is essential. This article discusses the perimeter of a rectangle, formulas, derivations, solved examples, and more. Read on to learn more!

Perimeter and Area of Rectangle

The Perimeter of a rectangle is defined as the sum of the length of all sides of a rectangle. To start with let’s recall the shape and structure of a rectangle. A rectangle is a quadrilateral with four sides. The opposite sides of a rectangle are parallel and of equal length. The angle made by the sides of a rectangle is 90 degrees and the diagonals of a rectangle are equal.

How To Find Perimeter of Rectangle?

It is important to know the formula for the perimeter of a rectangle. Go through the steps given below to arrive at the formula.

We know that Perimeter is the length of all sides of a closed figure. For rectangle the perimeter will be:

\({\rm{Perimeter}}\,{\rm{of}}\,{\rm{Rectangle = }}\,{\rm{Length}}\,{\rm{ + }}\,\,{\rm{Width}}\,\,{\rm{ + }}\,{\rm{Length}}\,\,{\rm{ + }}\,\,{\rm{Width}}\)

Derivation:

Let the length of the rectangle be ‘a’ units and the width be ‘b’ units as shown below:

Let the perimeter of the rectangle be ‘P’. Also, note that, the opposite sides of a rectangle are equal.

\({\rm{P}}\,{\rm{ = }}\,{\rm{Sum}}\,{\rm{of}}\,{\rm{all}}\,{\rm{its}}\,{\rm{four}}\,{\rm{sides}}\)

\({\rm{P}}\,{\rm{ = }}\,{\rm{a}}\,{\rm{ + }}\,{\rm{b}}\,{\rm{ + }}\,{\rm{a}}\,{\rm{ + }}\,{\rm{b}}\)

\({\rm{P}}\,{\rm{ = }}\,{\rm{2(a}}\,{\rm{ + }}\,{\rm{b)}}\)

Therefore,
\({\rm{Perimeter of}}\,{\rm{a rectangle}}\,{\rm{ = }}\,{\rm{2(length}}\,{\rm{ + }}\,{\rm{Width)square units}}\)

Perimeter of Rectangle Examples/ Solved Problems

Let’s go through the solved examples on the calculation of Perimeter of Rectangle from below:

Example 1: Calculate the perimeter of a rectangle whose length and width is \(5\,{\rm{cm}}\) to \(3\,{\rm{cm}}\) respectively.
Solution: As per the data given, the length is \(5\,{\rm{cm}}\) and the width is \(3\,{\rm{cm}}\) .
The perimeter of a rectangle \({\rm{ =  2 (length}}\,{\rm{ + }}\,{\rm{width)}}\)
Substitute the value of length and width here,
Perimeter, \({\rm{P}}\,{\rm{ = }}\,{\rm{2(5}}\,{\rm{ + }}\,{\rm{3)}}\,{\rm{cm}}\)
\({\rm{P}}\,{\rm{ = }}\,{\rm{2}}\,\, \times \,\,8\, = \,16\,{\rm{cm}}\,\)
Therefore, the perimeter of the rectangle is \(20\,{\rm{cm}}\) .

Example 2: Find the perimeter of a rectangle whose length and breadth are \(10\,{\rm{cm and 15}}\,{\rm{cm}}\)
Solution: As per the given data, the length is 10 cm and breadth is 15 cm.
The perimeter of a rectangle \({\rm{ =  2 (length}}\,{\rm{ + }}\,{\rm{width)}}\)
Substituting the values of length and breadth values.
\({\rm{P}}\,{\rm{ = }}\,{\rm{2(10}}\,{\rm{ + }}\,15{\rm{)}}\,\)
\({\rm{P}}\,{\rm{ = }}\,{\rm{2}}\,\, \times \,\,25\,\,\)
\({\rm{P}}\, = \,50\,{\rm{cm}}\)
Therefore, the perimeter of the rectangle is \(50\,{\rm{cm}}\)

Example 3: Find the length of the rectangle if the Perimeter is \(60\,{\rm{cm}}\) and the width is \({\rm{10}}\,{\rm{cm}}\).
Solution: As per the given data, Perimeter is \(60\,{\rm{cm}}\) and the width is \({\rm{10}}\,{\rm{cm}}\) .
Length of Rectangle
Length of Rectangle, \({\rm{L}}\, = (60\, – \,(2\,\, \times \,10))/2\)
\({\rm{L}}\, = (60\, – \,(2\,\, \times \,10))/2\)
\({\rm{L}} = 40/2\)
\({\rm{L}}\, = 20\,{\rm{cm}}\)
Therefore the length of the rectangle is \({\rm{20}}\,{\rm{cm}}\) .

Study Materials on Embibe

Make the use of following study materials from Embibe which will definitely help you in your exams:

FAQs on Perimeter of a Rectangle

Check the frequently asked questions on the perimeter of the rectangle from below:

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