Question

What happens to the area of the square when its side is halved? Its area will be
A.Remain same
B.Become half
C.Become one fourth
D.Become double

Answer 1

Hint: We know that the area of a square is given by ${\left( {side} \right)^2}$. So first let's consider a square with a side a and its area is ${a^2}$sq units. And one let's consider the square with the side halved that is $\dfrac{a}{2}$.

Complete step-by-step answer:
Step 1 :
Let's consider a square with side a
We know that the area of the square is given by ${\left( {side} \right)^2}$
Hence the area of the square with side a = ${a^2}$sq units
So this will be the area of our square.
Step 2 :
It is given that the side of the square is halved .
That is , the side of the square is divided by 2
Therefore , now the side of our new square is $\dfrac{a}{2}$
With this the area of our new square will be ${\left( {\dfrac{a}{2}} \right)^2} = \dfrac{{{a^2}}}{4}$sq units
Now we can see that when the side of the square is halved then the area of the square becomes one fourth of the area obtained with the original side.
Hence when the side of the square is halved then the area becomes one fourth
The correct option is C

Note: Each diagonal divides a square into two congruent isosceles right triangles.
Each of these right triangles has base and height both equal to the length of each side of the square. So, if the square has each side s units long, then the area of each triangle equals $\dfrac{1}{2}*s*s = \dfrac{1}{2}{s^2}$. Since the two triangles are congruent, they have equal area. Thus, the total area of the square is $\dfrac{1}{2}{s^2} + \dfrac{1}{2}{s^2} = {s^2}$sq units