Calculate the Area of a Square with Side Length 2⅓: Mixed Number Area Problem

To solve the problem of finding the area of a square with a side length of $2\frac{1}{3}$, we follow these steps:

• Step 1: Convert the side length to an improper fraction.
• Step 2: Use the formula for the area of a square.
• Step 3: Perform the necessary calculations and simplify.

Let's begin:

Step 1: Convert the mixed number $2\frac{1}{3}$ into an improper fraction. The conversion process involves multiplying the whole number part by the denominator and then adding the numerator:
$2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$.

Step 2: Use the area formula for a square, which is $\text{Area} = \text{side}^2$. Here, the side length is $\frac{7}{3}$, so we calculate:
$\text{Area} = \left(\frac{7}{3}\right)^2 = \frac{7 \times 7}{3 \times 3} = \frac{49}{9}$.

Step 3: Simplify or convert the improper fraction to a mixed number:
$\frac{49}{9}$ can be written as the mixed number $5\frac{4}{9}$.

Therefore, the area of the square is $5\frac{4}{9}$.