Perimeter of Square: Overview, Questions, Preparation

Square
A square is a quadrilateral having all four equal sides, and all the polygon's interior angles are right angles. It is a 2-dimensional plane structure.

Perimeter of Square

The perimeter of a square is the complete length of the boundaries. To measure the perimeter of a square, it is essential to add all the sides of the square.

The perimeter of a square is the addition of the four sides of the square. As all the four sides of the square are of equal length, the square's perimeter is four times the side.

The perimeter of a Square formula

The perimeter of Square (P) = four × side

Derivation of a Perimeter of Square

The perimeter of a square is the sum of the length of all its boundaries. Also, all sides are equal in the square so that formula will be,

Perimeter = side + side + side + side
Perimeter =4 x side

Hence the formula will be,
P= 4s
P= perimeter
s= length of one side of the square

Unit:
The unit to determine the value of the square of the perimeter can be millimetre (mm), centimetre (cm), metre (m), etc.

The perimeter of a square is an essential topic in the Mensuration chapter of maths NCERT. The topic holds importance in the Class 10 examination as the mark weightage is 5-8 marks. It is a formula-based topic and significantly scoring in the board exams. 

1. We have the measurements of a square and a rectangular field with the same perimeter. Which has the larger area?

Solution.        
Let's assume the breadth of the rectangle be x. The perimeter of the rectangle is equal to the perimeter of the given square in the question.

Therefore, 2(80+x) = 4×60
80 + x = 120
x = 120 – 80 = 40
i.e. breadth of the rectangle = 40 m

Area of the square = (60 × 60) m²
= 3600 m2

Area of the rectangle = (40 × 80) m²
= 3200 m²

Hence, the square field is larger than the rectangular field.

2. Mrs. Kaushik possesses a square plot with the stated measurements. She desires a house constructed in the middle of the plot. She also has a garden around the house. Determine the total cost of creating a garden with a rate of Rs. 55 per m².

Solution:
garden area = outer square area

Area of the inner rectangle
= 25 × 25 m2 = 20 × 15 m²
 (625 - 300) m2 = 325 m²

The cost of developing a garden at a price rate of Rs. 55 per sq. meter
= Rs. (55 × 325) = Rs. 17875

3. The lengths of the sides of a square are 11cm each. Determine the area and total length of its boundary.

Solution:
As, length of the side, a = 11 cm
Area = a2 = 112 = 121 sq.cm

Full length of boundary of square, Perimeter = 4a = 4 x 11 = 44 sq.cm.

Q: What is Perimeter?

Q: What is the formula for the perimeter of the square?

Q: What is the perimeter of a circle?

Q: What is the mark weightage of the perimeter of a square in the CBSE examination?

Q: How to prepare for the perimeter topic in the examination?