Perimeter and Area of Square



The formula of perimeter and area of square are explained step-by-step with solved examples.



If 'a' denotes the side of the square, then, length of each side of a square is 'a' units

perimeter and area of square

Perimeter of square = AB + BC + CD + DA
                           = (a + a + a + a) units
                           = 4a units

Perimeter of the square = 4a units

We know that the area of the square is given by
Area = side × side
A = a × a sq. units
Therefore, A = a2 square units
Therefore, a2 = A Here, a is the side of the square.
Therefore, a2 = √A
Therefore, side of the square = √Area

Side of the square = P/4 units
Area of the square = a × a = (P/4)2 sq. units
Area of square = 1/2 × (diagonal)2 sq. units
Length of the diagonal = √(a2 + a2) = √(2a2^2) = a√2 units



Worked-out examples on Perimeter and Area of the Square:

1. Find the perimeter and area of a square of side 11 cm.

Solution:

We know that the perimeter of square = 4 × side
Side= 11 cm
Therefore, perimeter = 4 × 11 cm = 44 cm
Now, area of the square = (side × side) sq. units
                      = 11 × 11 cm2
                      = 121 cm2


2. The perimeter of a square is 52 m. Find the area of the square.

Solution:

Perimeter of square = 52 m
But perimeter of square = 4 × side
Therefore, 4 × side = 52 m
Therefore, side= 52/4 m = 13m
Now, the area of the square = (side × side)
Therefore, area of the square = 13 × 13 m2 = 169 m2


3. The area of a square is 144 m2. Find its perimeter.

Solution:

Area of square = side × side
Given; area of square = 144 m2
Therefore, side2 = 144 m2
Therefore, side = √(144 m2) = √(2 × 2 × 2 × 2 × 3 × 3) m2 = 2 × 2 × 3 m = 12 m
Now, the perimeter of the square = 4 x side = 4 × 12 m = 48 m


4. The length of the diagonal of a square is 12 cm. Find its area and perimeter.

Solution:

Diagonal of a square = 12 cm
Area of square = 1/2 (d)2
= 1/2 (12)2
= 1/2 × 12 × 12
= 72
Side of a square = √Area
= √72
= √(2 × 2 × 2 × 3 × 3)
=2 × 3√2
= 6 × 1.41
= 8.46 cm
Perimeter of square = 4 × 8.46 = 33.84 cm


5. The perimeter of a square courtyard is 144 m. Find the cost of cementing it at the rate of $5 per m2.

Solution:

Perimeter of square courtyard = 144 m
Therefore, side of the square courtyard = 144/4 = 36 m
Therefore, area of square courtyard = 36 × 36 m2 = 1296 m2
For 1 m2, the cost of cementing = $5
For 1296 m2, the cost of cementing = $1296 × 5 = $6480

The above solved examples are explained how to solve perimeter and area of square with the detailed explanation.



Mensuration

  • Area and Perimeter
  • Perimeter and Area of Rectangle
  • Perimeter and Area of Square
  • Area of the Path
  • Area and Perimeter of the Triangle
  • Area and Perimeter of the Parallelogram
  • Area and Perimeter of Rhombus
  • Area of Trapezium
  • Circumference and Area of Circle
  • Units of Area Conversion
  • Practice Test on Area and Perimeter of Rectangle
  • Practice Test on Area and Perimeter of Square

  • Mensuration - Worksheets
  • Worksheet on Area and Perimeter of Rectangles
  • Worksheet on Area and Perimeter of Squares
  • Worksheet on Area of the Path
  • Worksheet on Circumference and Area of Circle
  • Worksheet on Area and Perimeter of Triangle




  • 7th Grade Math Problems

    8th Grade Math Practice

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