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

Options

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

Answer

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

### Step 1: Understand the original area of the square
Let the original side length of the square be \( a \). The area \( A \) of the square is given by the formula:
\[ A = a^2 \]

### Step 2: Calculate the new side length after the increase
If each side is increased by 10%, the new side length \( a' \) can be calculated as:
\[ a' = a + 0.1a = 1.1a \]

### Step 3: Calculate the new area of the square
Now, we can find the new area \( A' \) using the new side length:
\[ A' = (a')^2 = (1.1a)^2 = 1.21a^2 \]

### Step 4: Determine the increase in area
The increase in area can be calculated by subtracting the original area from the new area:
\[ \text{Increase in Area} = A' - A = 1.21a^2 - a^2 = 0.21a^2 \]

### Step 5: Calculate the percentage increase in area
To find the percentage increase in area, we use the formula:
\[ \text{Percentage Increase} = \left(\frac{\text{Increase in Area}}{\text{Original Area}}\right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Increase} = \left(\frac{0.21a^2}{a^2}\right) \times 100 = 0.21 \times 100 = 21\% \]

### Conclusion
The percentage increase in the area of the square when each side is increased by 10% is **21%**.

---