# 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 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

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
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