Question

What will happen to the area of a square if its side is doubled and halved:

Answer 1

Square with side ${}^{\prime }{a}^{\prime }$

Area of the original square $=(side{)}^2=a^2$

(i) if side is doubled, we have

Then, New side $=2a$

New area of the square $=\left(2a\right)\left(2a\right)$

$=4a^2$

$=4\times$ area of the original square

(ii) if side is halved, then

New side $=\frac{a}{2}$

New area of the square $=\left(\frac{a}{2}\right)\left(\frac{a}{2}\right)$

$=\frac{a^2}{4}$

$=\frac{1}{4}\times$ area of the original square