What will be the percentage increase in the area of a square when each of the its sides is increased by `10%` ?

Options

A. 20
B. 11
C. 121
D. 21

Answer

To find the percentage increase in the area of a square when each of its sides is increased by 10%, we can follow these steps:

### Step 1: Define the original side length
Let the original side length of the square be \( s \).

### Step 2: Calculate the original area
The area \( A_1 \) of the square can be calculated using the formula:
\[ A_1 = s^2 \]

### Step 3: Calculate the new side length after a 10% increase
If each side is increased by 10%, the new side length \( s' \) can be calculated as:
\[ s' = s + 0.1s = 1.1s \]

### Step 4: Calculate the new area
Now, we calculate the new area \( A_2 \) using the new side length:
\[ A_2 = (s')^2 = (1.1s)^2 = 1.21s^2 \]

### Step 5: Calculate the increase in area
The increase in area \( \Delta A \) is given by:
\[ \Delta A = A_2 - A_1 = 1.21s^2 - s^2 = 0.21s^2 \]

### Step 6: Calculate the percentage increase
To find the percentage increase in area, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{\Delta A}{A_1} \right) \times 100 = \left( \frac{0.21s^2}{s^2} \right) \times 100 = 21\% \]

Thus, the percentage increase in the area of the square when each of its sides is increased by 10% is **21%**.

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