Side of a square is first increased by 10% and then decreased by 20%. What is the overall percentage change in area?

Decrease by 22.56%

Concept,

If x and y are the changes in the measurements of length and breadth then,

Change % = x + y + \(\frac{xy}{100}\) 

= Change % in length of side = 10 – 20 + \(\frac{10 × (– 20)}{100}\) = 10 – 20 – 2 = – 12%

Again,

= Change % in area of square = – 12 – 12 + \(\frac{(– 12) × (– 12)}{100}\) = – 24 + 1.44 = – 22.56% ( Decreased)