To determine the perimeter of a square given its area, follow these steps:
1. Identify the area of the square: The problem states that the area is [tex]\(64 \, \text{cm}^2\)[/tex].
2. Express the area in terms of the side length: The area [tex]\(A\)[/tex] of a square is given by [tex]\(A = \text{side}^2\)[/tex], where [tex]\(\text{side}\)[/tex] refers to the length of one side of the square.
3. Calculate the side length: Since the area is [tex]\(64 \, \text{cm}^2\)[/tex], set up the equation:
[tex]\[
\text{side}^2 = 64
\][/tex]
Solve for the side length by taking the square root of both sides:
[tex]\[
\text{side} = \sqrt{64} = 8 \, \text{cm}
\][/tex]
4. Determine the perimeter: The perimeter [tex]\(P\)[/tex] of a square is given by [tex]\(P = 4 \times \text{side}\)[/tex]. Using the side length calculated:
[tex]\[
P = 4 \times 8 \, \text{cm} = 32 \, \text{cm}
\][/tex]
Therefore, the perimeter of the square is [tex]\(32 \, \text{cm}\)[/tex].
