Question

What will be the change in the area of a square if its side is 

(i) Halved? 

(ii) Doubled?

Answer 1

(i) (let) Side of square = a 

Then, Area = a × a = a² 

If length of side = (1/2) × a = a/2

Then Area = a/2 a/2 = a²/4 

= (1/4)a² = 1/4 = (initial area) 

Thus, New area, remains one fourth of initial area. 

(ii) Side of square (let) = a 

Then area = a × a = a² if length doubled, then side = 2a and 

Area = 2a × 2a = 4a² 

= 4(a²) = 4 (initial area) 

Thus, New area, became four times of initial area.