The side of the square is increased by 20% then what is the % change in its area?

Options

A. `54%`
B. `34%`
C. `52%`
D. `44%`

Answer

To find the percentage change in the area of a square when the side is increased by 20%, we can follow these steps:

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

### Step 2: Calculate the new side after the increase
If the side is increased by 20%, the new side \( s' \) can be calculated as:
\[ s' = s + 0.2s = 1.2s \]

### Step 3: Calculate the new area of the square
Now, we need to find the new area \( A' \) with the new side:
\[ A' = (s')^2 = (1.2s)^2 = 1.44s^2 \]

### Step 4: Find the change in area
The change in area can be calculated as:
\[ \text{Change in area} = A' - A = 1.44s^2 - s^2 = 0.44s^2 \]

### Step 5: Calculate the percentage change in area
The percentage change in area can be calculated using the formula:
\[ \text{Percentage change} = \left( \frac{\text{Change in area}}{\text{Original area}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage change} = \left( \frac{0.44s^2}{s^2} \right) \times 100 = 44\% \]

Thus, the percentage change in the area of the square when the side is increased by 20% is **44%**.