A square is of side `3 (3)/(4)` m. Find the area of the square.

Answer

To find the area of a square with a side length of \(3 \frac{3}{4}\) meters, we can follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
The side length of the square is given as \(3 \frac{3}{4}\). To convert this mixed fraction into an improper fraction, we can use the formula:

\[ \text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator} + \text{Numerator}\right) / \text{Denominator} \]

Here, the whole number is 3, the numerator is 3, and the denominator is 4.

Calculating this gives:

\[ 3 \frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4} \]

### Step 2: Calculate the area of the square
The area \(A\) of a square is given by the formula:

\[ A = a^2 \]

where \(a\) is the side length of the square. Substituting the value we found:

\[ A = \left(\frac{15}{4}\right)^2 \]

Calculating this gives:

\[ A = \frac{15 \times 15}{4 \times 4} = \frac{225}{16} \]

### Step 3: Convert the area from an improper fraction to a mixed fraction
To convert \(\frac{225}{16}\) into a mixed fraction, we divide 225 by 16.

Calculating this gives:

\[ 225 \div 16 = 14 \quad \text{(since } 16 \times 14 = 224\text{)} \]

The remainder is:

\[ 225 - 224 = 1 \]

Thus, we can express \(\frac{225}{16}\) as:

\[ 14 \frac{1}{16} \]

### Final Answer
The area of the square is \(14 \frac{1}{16}\) square meters.

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