To find the area of a square given its perimeter, we'll follow a step-by-step process:
1. Understand the relationship between the perimeter and the side length of a square.
The perimeter [tex]\( P \)[/tex] of a square is calculated by summing the lengths of all four sides. Since all four sides of a square are equal in length, if we let [tex]\( s \)[/tex] be the side length, then:
[tex]\[
P = 4s
\][/tex]
2. Set up the equation using the given perimeter.
Given:
[tex]\[
P = 24
\][/tex]
Plugging in the known perimeter:
[tex]\[
24 = 4s
\][/tex]
3. Solve for the side length [tex]\( s \)[/tex].
To find [tex]\( s \)[/tex], divide both sides of the equation by 4:
[tex]\[
s = \frac{24}{4} = 6
\][/tex]
4. Calculate the area of the square once you know the side length.
The area [tex]\( A \)[/tex] of a square is given by the square of its side length:
[tex]\[
A = s^2
\][/tex]
Substituting the side length [tex]\( s = 6 \)[/tex] into the formula:
[tex]\[
A = 6^2 = 36
\][/tex]
Therefore, the area of the square is [tex]\( 36 \)[/tex] square units.
