The diagonal length of a square is 14.1 sq. units. What is the area of the square, rounded to the nearest integer?

Options

A. 96
B. 98
C. 98
D. 100

Answer

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

### Step 1: Understand the relationship between the diagonal and the side of the square.
The diagonal \(d\) of a square is related to its side length \(a\) by the formula:
\[ d = a\sqrt{2} \]

### Step 2: Substitute the given diagonal length into the formula.
Given that the diagonal length \(d\) is 14.1 units, we can set up the equation:
\[ 14.1 = a\sqrt{2} \]

### Step 3: Solve for the side length \(a\).
To find \(a\), we can rearrange the equation:
\[ a = \frac{14.1}{\sqrt{2}} \]

### Step 4: Calculate \(a\).
Now, we need to compute \(a\):
\[ a = \frac{14.1}{\sqrt{2}} \approx \frac{14.1}{1.414} \approx 9.95 \text{ (approximately)} \]

### Step 5: Calculate the area of the square.
The area \(A\) of the square is given by:
\[ A = a^2 \]
Now, we can calculate \(A\):
\[ A \approx (9.95)^2 \approx 99.0025 \]

### Step 6: Round the area to the nearest integer.
Rounding \(99.0025\) to the nearest integer gives us:
\[ A \approx 99 \]

### Final Answer:
The area of the square, rounded to the nearest integer, is **99 square units**.

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