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

Let the side of the square be 100

side increased by 10%

then S1 = $$ 100 +( \frac{10}{100} \times 100 ) $$

               = 110

The resultant side then decreased by 20%

S2 = $$ 110 - ( \frac{20}{100} \times 110 ) $$

    = 88

A1 = $$ S1^2 $$

     = 12100

A2 = $$ S2^2 $$

     = 7744

A2 < A1. That means the area is decreased from initially. Hence the change will also be a decrease.

overall percentage change in area = $$ \frac{10000 - 7744}{10000} \times 100 $$

= 22.56%