Side of square = 5 cm. How many times does area increase if side is doubled?
Step 1: Formula — \(\text{Area of a square} = \text{side} \times \text{side}\).
Step 2: Original side = \(5\,\text{cm}\).
Original area = \(5 \times 5 = 25\,\text{cm}^2\).
Step 3: The side is doubled.
New side = \(2 \times 5 = 10\,\text{cm}\).
Step 4: New area = \(10 \times 10 = 100\,\text{cm}^2\).
Step 5: How many times bigger?
\(\dfrac{\text{New area}}{\text{Original area}} = \dfrac{100}{25} = 4\).
Conclusion: The area becomes 4 times the original.
Quick rule: If the side is multiplied by \(k\), the area is multiplied by \(k^2\). Here, \(k=2\) so \(2^2=4\).