Question

What happens to the area of a square if its side is halved?

Answer 1

Step 1:

Area of initial square$=side\times side$

Let the side of the square be $xunit$

Area of square$=x\times x=x^{2}unitsquare$

Step 2:

Side of new square when halved$=\frac{x}{2}$

Area of new square when halved$=\frac{x}{2}\times \frac{x}{2}=\frac{x^2}{4}unitsquare$

Step 3:

Impact on area when side is halved$=\frac{Areaofnewsquare}{Areaofinitialsquare}=\frac{{\displaystyle \frac{x^2}{4}}}{x^2}=\frac{1}{4}times$

Hence, area of square becomes $\frac{1}{4}times$ times when side is halved.