Perimeter of Rectangle Formula, Questions for Class 5

Perimeter of Rectangle

Perimeter of Rectangle: A closed path that includes, encircles, or outlines a two-dimensional shape is known as a perimeter. The perimeter of  Rectangle basically defines the total area that it covers around its edge. A rectangle is a quadrilateral with four right angles at the vertices and two pairs of parallel sides of equal length. In this article, we are going to learn about Perimeter of Rectangle, and its formula with some solved examples.

Check: Perimeter of Square and Its Formula

What is Perimeter of Rectangle?

Before learning the formula of the Perimeter of rectangle, we must understand the properties of a Rectangle. As the name suggests a rectangle is a four-sided quadrilateral. A rectangle’s opposite sides are parallel and equal in length. A rectangle has four angles because it has four sides. A rectangle’s angles are all equal, which is 90 degrees. Another feature of the rectangle is that it has two equal-length diagonals.

Any polygon’s perimeter is equal to the sum of the lengths of its sides. The total distance travelled when going around a rectangle in its entire length is its perimeter. As The perimeter of rectangle can be described as the sum of the length of all four sides in a rectangle.

The perimeter of rectangle is calculated using the formula perimeter of a rectangle = 2(l + w), where l is the rectangle’s length and w is its width.

Read: Pythagoras’s theorem

Rectangle Formulas

The formula for calculating the area and perimeter of a rectangle is as follows:

1. Area of a Rectangle: The area (A) of a rectangle is given by the formula:

   A = length × width

   where:

   • “Length” is the length of the rectangle.
   • “Width” is the width of the rectangle.
2. The perimeter of a Rectangle: The perimeter (P) of a rectangle is given by the formula:

   P = 2 × (length + width)

   where:

   • “Length” is the length of the rectangle.
   • “Width” is the width of the rectangle.

These formulas are used to calculate the area and perimeter of rectangles, which are four-sided geometric shapes with opposite sides of equal length and right angles.

Perimeter of Rectangle Formula

In geometry, Perimeter of the Rectangle formula is one of the basic formulae of the Rectangle. Earlier we came to know that the Perimeter of a Rectangle is the sum of the total length of all the sides of the rectangle. The formula to determine the perimeter of a rectangle is written below:

Perimeter of  Rectangle= Sum of lengths of four sides

Perimeter of  Rectangle = length + length + width + width

P = l + l + w + w

Or, P = 2 (l + w)

Therefore we can conclude that, the formula for the perimeter of rectangle, P = 2 × (length + width) = 2 × (sum of adjacent sides)

Derivation of Perimeter of Rectangle Formula

The derivation of the Perimeter of the formula is very simple. We can obtain the perimeter of any polygon by adding all sides. While determining a perimeter of a Rectangle, we know that sides opposite to each other have equal lengths.Let’s assume, the length and width of a rectangle are ‘a’, and’ b’. Consequently, the perimeter (P) of that rectangle is given by

P = the sum of its four sides.
P = a + b + a + b (Opposite sides of a rectangle are equal)
P = 2(a + b)
Therefore,

Perimeter of a rectangle = 2(Length + Width)  unit

Steps to Calculate the Perimeter of a Rectangle

The perimeter of a rectangle can be calculated in three simple steps. The three steps listed below will help you calculate the perimeter of a Rectangle.

Step 1: To calculate the perimeter of a rectangle, first determine the length and width of the given rectangle.
Step 2: The length and width values are substituted in the perimeter of a rectangle formula.
Step 3: After solving the equation, the perimeter of the given rectangle value is calculated.

Read: Area of Equilateral Triangle Formula

Perimeter of Rectangle Application

The perimeter of a rectangle has numerous real-life applications

• We must use concrete to set a boundary for the house’s construction plan, which is made possible by the perimeter formula.
• The perimeter formula can be used to calculate the length of a rectangular field or garden for its fencing.
• It can be used for a variety of arts and crafts tasks, such as decorating the edge of rectangular cardboard with vibrant ribbons or ropes.

Perimeter of Rectangle Questions for Class 5

Q. The perimeter and width of a perimeter is 60 cm and 10 cm respectively. Determine the length of that rectangle.

Solution: Given here,
The perimeter of the rectangle is 60 cm, Width is 10 cm.
Let’s assume the one side’s  length of  the rectangle is L
The formula for determining the perimeter of the rectangle is 
P = 2(length + width)
Or, 60 = 2 (L+ 10) 
Or, L+ 10 = 60/2 
Or, L + 10 = 30 
Or, L = 30 -10 = 20 cm.
Hence, the length of that. the rectangle’s one side is 20 cm.

Q. Find the area and perimeter of rectangle having a length of 12 cm and a width of 8 cm.

Solution: In the given rectangle, Length = 12 cm and width =8 cm
Therefore,
The perimeter of a rectangle = 2(length + width)
Now, 
The perimeter of the given rectangle is 
Perimeter, P = 2(12 + 8) cm
P = 2 x 20 cm
P = 40 Cm.
Therefore, the perimeter of a rectangle is 40 cm.
Now, the Formula for calculating the area of rectangle A is.
Area of a rectangle = (length × width) square units.
Or, A = (12 × 8) cm²
A = 96 cm²
Therefore, the Area of a rectangle is 96 cm²

Q.Calculate the perimeter of a rectangular park whose length and width are 10 m  and 6 m, respectively.If the fencing cost is 50 rupees per meter. Then what is the total cost of fencing the park? 

Solution:
Given:
Length of the park  = 10 m and Width = 6 cm
Earlier we know that
The perimeter of a rectangle = 2(length + width)
Now, 
The perimeter of the given rectangular park is 
Perimeter, P = 2(10+ 6) m
P = 2 x 16 m
P= 32 m
Therefore, the perimeter of a rectangular park is 32 m.

Now,  the fencing cost is 50 rupees per meter. Then, the total cost for fencing the park is .
= (Perimeter of park × per meter fencing cost)
= 32 m× 50 rupees
= 1600 rupees.