Answer:
If each side of a square is decreased to one third of its original length, the new side length becomes \(\frac{1}{3}\) of the original length. The area of a square is proportional to the square of its side length.
So, if the side length is reduced to \(\frac{1}{3}\), the new area will be \(\left(\frac{1}{3}\right)^2\) times the original area.
\[ \text{New Area} = \left(\frac{1}{3}\right)^2 \times \text{Original Area} \]
Simplifying this expression:
\[ \text{New Area} = \frac{1}{9} \times \text{Original Area} \]
Therefore, the area of the square will be decreased to \(\frac{1}{9}\) of its original area.
