If each side of a square be increased by 10%, the percentage increase in area is

Given:

Side of a square increased = 10%

Formula used:

Increase = New number - Original number

% increase = (Increase/Original Number) × 100

Area of square = side2

Calculations:

Let the side of the square be a 

Area of a square with side a = a²

After increasing percentage of side a by 10% = a + 10% of a

⇒ a(1 + 10/100) = a(1 + 1/10)

⇒ a(11/10) = 11a/10

Area of the square after increasing side by a = (11a/10)²

⇒ (11a/10) × (11a/10) = 121a²/100

⇒ 1.21a²

Percentage change in area of square =[(1.21a² - a²)/a²] × 100

⇒ [a²(1.21 - 1)/a²] × 100 = 0.21 × 100 

⇒ 21%

∴ Percentage change in area of square is 21%

Alternate Method

Percentage increase in a regular polygon = x + y + (xy/100)

In square length and breadth are same, x = y

Percentage increase = x + x + (xx/100)

⇒ 2x + x²/100 = 2 × 10 + 10 × 10/100

⇒ 20 + 1 = 21%

∴ The required percentage is 21%