Each side of a square is increased by `10%` . The percentage increase of its area is :

Options

A. 20
B. 25
C. 21
D. 12.5

Answer

To solve the problem of finding the percentage increase in the area of a square when each side is increased by 10%, we can follow these steps:

### Step-by-Step Solution:

1. **Let the original side length of the square be \( x \) cm.**
- **Hint:** Define a variable for the side length to simplify calculations.

2. **Calculate the original area of the square.**
\[ \text{Original Area} = \text{side}^2 = x^2 \text{ cm}^2 \]
- **Hint:** Remember that the area of a square is given by the square of its side length.

3. **Determine the new side length after a 10% increase.**
- A 10% increase means the new side length is:
\[ \text{New Side} = x + 0.1x = 1.1x \]
- **Hint:** To find a percentage increase, multiply the original value by the percentage in decimal form.

4. **Calculate the new area of the square with the increased side length.**
\[ \text{New Area} = (1.1x)^2 = 1.21x^2 \text{ cm}^2 \]
- **Hint:** Use the formula for the area of a square with the new side length.

5. **Find the increase in area.**
\[ \text{Increase in Area} = \text{New Area} - \text{Original Area} = 1.21x^2 - x^2 = 0.21x^2 \text{ cm}^2 \]
- **Hint:** Subtract the original area from the new area to find the increase.

6. **Calculate the percentage increase in area.**
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in Area}}{\text{Original Area}} \right) \times 100 = \left( \frac{0.21x^2}{x^2} \right) \times 100 = 21\% \]
- **Hint:** To find the percentage, divide the increase by the original and multiply by 100.

### Final Answer:
The percentage increase in the area of the square is **21%**.