If the side of a square is increased by 25%, then its area is increased by :

Options

A. `25%`
B. `55%`
C. `40.5%`
D. `56.25%`

Answer

To solve the problem, we need to determine how much the area of a square increases when its side length is increased by 25%.

### Step-by-Step Solution:

1. **Understand the original side length**:
Let the original side length of the square be \( s \).

2. **Calculate the new side length**:
If the side length is increased by 25%, the new side length \( s' \) can be calculated as:
\[ s' = s + 0.25s = 1.25s \]

3. **Calculate the original area**:
The area \( A \) of the original square is given by:
\[ A = s^2 \]

4. **Calculate the new area**:
The area \( A' \) of the new square with the increased side length is:
\[ A' = (s')^2 = (1.25s)^2 = 1.5625s^2 \]

5. **Determine the increase in area**:
The increase in area can be calculated as:
\[ \text{Increase in area} = A' - A = 1.5625s^2 - s^2 = 0.5625s^2 \]

6. **Calculate the percentage increase in area**:
The percentage increase in area is given by:
\[ \text{Percentage increase} = \left( \frac{\text{Increase in area}}{A} \right) \times 100 = \left( \frac{0.5625s^2}{s^2} \right) \times 100 = 56.25\% \]

### Conclusion:
Thus, if the side of a square is increased by 25%, its area is increased by **56.25%**.

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