If all the sides of a square are increased by 20%, then area is increased by

Options

A. a. 46%
B. b. 44%
C. c. 43%
D. d. 45%

Answer

To solve the problem of how much the area of a square increases when all its sides are increased by 20%, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the original side length of the square**:
Let’s assume the side length of the square is \( s \). For simplicity, we can take \( s = 10 \) units.

2. **Calculate the increase in side length**:
The side length is increased by 20%.
\[ \text{Increase} = s \times \frac{20}{100} = 10 \times 0.2 = 2 \text{ units} \]

3. **Calculate the new side length**:
The new side length after the increase is:
\[ \text{New side length} = s + \text{Increase} = 10 + 2 = 12 \text{ units} \]

4. **Calculate the original area of the square**:
The area of a square is given by the formula \( \text{Area} = s^2 \). Therefore, the original area is:
\[ \text{Old Area} = 10^2 = 100 \text{ square units} \]

5. **Calculate the new area of the square**:
Using the new side length, the new area is:
\[ \text{New Area} = (12)^2 = 144 \text{ square units} \]

6. **Calculate the increase in area**:
The increase in area is:
\[ \text{Increase in Area} = \text{New Area} - \text{Old Area} = 144 - 100 = 44 \text{ square units} \]

7. **Calculate the percentage increase in area**:
To find the percentage increase, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in Area}}{\text{Old Area}} \right) \times 100 = \left( \frac{44}{100} \right) \times 100 = 44\% \]

### Final Answer:
The area of the square is increased by **44%**.