Question

What will happen to the area of a square when
(a) its side is doubled
(b) its side is halved

Answer 1

hey mate...
formula of..., area of square = ( side) ^2
a.) Now if we double the side...
area of square = ( 2 * side) ^2 = 4 ( Side) ^2
So., area will also increase with double.

b.) Now if we half the side
area of square = (side / 2)^2 = 1/4 (side) ^2

So., area will be decrease by 4....
⚡⚡hope it will helpful⚡⚡

Answer 2

What will happen to the area of a square when

(a) It's side is doubled

SOLUTION :

First of all about square -

SQUARE : A polygon which has 4 squad sides

                 All 4 interior angles = 90° each

The area = $\bf{ a^{2} }$ unit sq.

The perimeter = 4a unit

[ ∴ In which a is the side of the square ]

Now,

if we double the side of the square we will get

= 2a units

So,

new area of the square will be = $\bf{ (2a)^{2} }$ unit sq.

= $\bf{ {4a}^{2} }$ unit sq.

= $\bf{ 4 \times a^{2} }$ unit sq.

Hence

the area the square will be increased by 4 times if the side of the square is doubled

_________________________________________

What will happen to the area of a square when

(b) It's side is halved

SOLUTION :

We know that area of square = $\bf{ a^{2} }$ unit sq.

If the side Area halved,

side = $\frac{1}{2}$ × a  =  $\frac{a}{2}$ unit

Now,

new area of square will be = $\bf{ (\frac{a}{2} )^{2} }$ unit sq.

= $\bf {( {\frac{ a^{2} }{4}) }}$ unit sq.

= $\frac{1}{4}$ × ${a}^{2}$  unit sq.

Hence,

The area of the square will be one-fourth, if the side of the square is halved