Question

If the sides of a square are halved, the its area

(a) remains same
(b) becomes half
(c) becomes one fourth
(d) becomes double

Answer 1

(c) becomes one fourth

Let the side of the square be x.

Then, area = (Side $\times$ Side) = (x $\times$ x) = x²

If the sides are halved, new side = $\frac{x}{2}$

Now, new area = ${\left(\frac{x}{2}\right)}^2$= $\frac{x^2}{4}$

It is clearly visible that the area has become one-fourth of its previous value.