If the side of the square increases by 40%, then the area of the square…

Concept

When the side length of a square is multiplied by a factor k, its area is multiplied by k2 because A = s2.

Therefore, the percentage change in area is (k2 − 1) × 100%.

Application

1. Let the original side be s; the original area is s2.

2. A 40% increase makes the new side 1.4s.

3. The new area is (1.4s)2 = 1.96s2.

4. The increase is 1.96s2 − s2 = 0.96s2; therefore, the percentage increase is 96%.

Cross-check

If s = 10, the area changes from 100 to 196, an increase of 96 on a base of 100.

Result: the area increases by 96%.