If the side of a square is tripled, find the new area.

Answer

To solve the problem of finding the new area of a square when its side is tripled, we can follow these steps:

### Step 1: Understand the formula for the area of a square
The area \( A \) of a square is calculated using the formula:
\[ A = \text{side} \times \text{side} = \text{side}^2 \]

### Step 2: Define the original side length
Let the original side length of the square be \( a \).

### Step 3: Calculate the original area
Using the formula from Step 1, the original area \( A_{\text{original}} \) of the square can be calculated as:
\[ A_{\text{original}} = a^2 \]

### Step 4: Determine the new side length
If the side of the square is tripled, the new side length \( a_{\text{new}} \) will be:
\[ a_{\text{new}} = 3a \]

### Step 5: Calculate the new area
Now, we can find the new area \( A_{\text{new}} \) using the new side length:
\[ A_{\text{new}} = a_{\text{new}} \times a_{\text{new}} = (3a) \times (3a) = 9a^2 \]

### Step 6: Compare the new area with the original area
We can see that the new area \( A_{\text{new}} \) is:
\[ A_{\text{new}} = 9a^2 \]
This means the new area is 9 times the original area:
\[ A_{\text{new}} = 9 \times A_{\text{original}} \]

### Conclusion
The new area of the square, when its side is tripled, is \( 9a^2 \).

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