What happens to the area of the square when its side is halved

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{Let} \mathrm{side} \mathrm{be} \mathrm{square} \mathrm{be} \text{'}\mathrm{a}\text{'} \mathrm{units}. \\ \Rightarrow \mathrm{Area} \mathrm{of} \mathrm{square}=\mathrm{a}\times \mathrm{a}={\mathrm{a}}^2 {\mathrm{unit}}^2 \\ \mathrm{As} \mathrm{side} \mathrm{is} \mathrm{halved}, \mathrm{hence} \mathrm{new} \mathrm{square} \mathrm{will} \mathrm{have} \mathrm{sides} \mathrm{of} \frac{\mathrm{a}}{2} \mathrm{units} \\ \mathrm{New} \mathrm{area}=\left(\frac{\mathrm{a}}{2}\right)\times \left(\frac{\mathrm{a}}{2}\right)=\frac{{\mathrm{a}}^2}{4}=\frac{\mathrm{Original} \mathrm{Area}}{4} \\ \mathrm{Hence} \mathrm{if} \mathrm{side} \mathrm{of} \mathrm{square} \mathrm{is} \mathrm{halved}, \mathrm{then} \mathrm{area} \mathrm{becomes} \frac{1}{4} \mathrm{of} \mathrm{original} \mathrm{area}. \end{gathered}$$

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