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.

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