To find the area of a square given its perimeter, let's proceed step-by-step.
1. Understanding the Perimeter:
The given perimeter of the square is [tex]\(9 \frac{1}{11} \text{ meters}\)[/tex]. First, we convert this mixed number into an improper fraction for simplicity in our calculations:
[tex]\[
9 \frac{1}{11} = \frac{9 \times 11 + 1}{11} = \frac{99 + 1}{11} = \frac{100}{11} \text{ meters}
\][/tex]
2. Finding the Side Length:
The perimeter of a square is calculated as four times its side length. Let [tex]\( s \)[/tex] be the side length of the square.
[tex]\[
4s = \frac{100}{11}
\][/tex]
To find [tex]\( s \)[/tex], we divide both sides of the equation by 4:
[tex]\[
s = \frac{100}{11} \div 4 = \frac{100}{11} \times \frac{1}{4} = \frac{100}{44} = \frac{25}{11} \text{ meters}
\][/tex]
3. Calculating the Area:
The area [tex]\(A\)[/tex] of a square is given by the square of its side length:
[tex]\[
A = s^2
\][/tex]
Substituting the value of [tex]\( s \)[/tex]:
[tex]\[
A = \left(\frac{25}{11}\right)^2 = \frac{25 \times 25}{11 \times 11} = \frac{625}{121} \text{ square meters}
\][/tex]
Converting [tex]\(\frac{625}{121}\)[/tex] to a decimal, we get:
[tex]\[
\frac{625}{121} \approx 5.165289256198348 \text{ square meters}
\][/tex]
4. Conclusion:
Therefore, the area of the square is approximately [tex]\(\boxed{5.165289256198348 \text{ square meters}}\)[/tex].
In summary:
- Side length: [tex]\( \approx 2.272727272727273 \text{ meters} \)[/tex]
- Area: [tex]\( \approx 5.165289256198348 \text{ square meters} \)[/tex]
