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if the painted part of the square is 32cm² what is the size of the square side

To solve this problem, we need to assume that the painted area is within the square, and this area is mentioned as \( 32 \, \text{cm}^2 \).

Let's assume that the entire square is painted, meaning that the area of the square equals the painted area.

The area \( A \) of a square is given by the formula:

\[
A = s^2
\]

where \( s \) is the length of a side of the square. Given that the painted area is \( 32 \, \text{cm}^2 \), we can set up the equation:

\[
s^2 = 32 \, \text{cm}^2
\]

To find the side length \( s \), we take the square root of both sides:

\[
s = \sqrt{32} \, \text{cm}
\]

\[
s = \sqrt{16 \times 2} \, \text{cm} = 4\sqrt{2} \, \text{cm} \approx 5.66 \, \text{cm}
\]

So, the length of the side of the square is approximately \( 5.66 \, \text{cm} \).

Would you like more details or have any questions? Here are some related questions to explore further:

1. What would be the side length of the square if the area was 64 cm²?
2. If the square's side length was 10 cm, what would its area be?
3. How would the side length change if the area of the square were quadrupled?
4. What is the area of a square with a side length of 7 cm?
5. How does the perimeter of the square relate to its area?

**Tip:** Remember, the area of a square increases quadratically as the side length increases, meaning a small increase in side length results in a larger increase in area.

Learn how to find the side length of a square when given its painted area of 32 cm². This problem involves using the formula for the area of a square and understanding square roots. Suitable for students in Grades 7-9.

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