Each side of a square is `5 2/3` m long. Find its area.

Answer

To find the area of a square when each side is given, we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The length of each side of the square is given as \(5 \frac{2}{3}\) meters. First, we need to convert this mixed number into an improper fraction.

\[ 5 \frac{2}{3} = \frac{(5 \times 3) + 2}{3} = \frac{15 + 2}{3} = \frac{17}{3} \]

### Step 2: Use the formula for the area of a square
The area \(A\) of a square is calculated using the formula:
\[ A = \text{side} \times \text{side} \]
Since each side is \( \frac{17}{3} \) meters, we can substitute this into the formula:
\[ A = \left(\frac{17}{3}\right) \times \left(\frac{17}{3}\right) \]

### Step 3: Multiply the fractions
To multiply the fractions, we multiply the numerators and the denominators:
\[ A = \frac{17 \times 17}{3 \times 3} = \frac{289}{9} \]

### Step 4: State the area in square meters
The area of the square is therefore:
\[ A = \frac{289}{9} \text{ square meters} \]

### Final Answer
The area of the square is \( \frac{289}{9} \) m².

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