The sides of a rectangle are 7.01 m and `1.2xx10^(1)m`. Taking the significant figures into account, the area of the rectangle is

Options

A. `84.1m^(2)`
B. `84.00m^(2)`
C. `84.12m^(2)`
D. `84m^(2)`

Answer

To find the area of a rectangle given its sides, we can follow these steps:

### Step 1: Identify the dimensions of the rectangle
The given dimensions of the rectangle are:
- Length = 7.01 m
- Width = 1.2 x 10^1 m = 12 m

### Step 2: Determine the number of significant figures
- For the length (7.01 m), the significant figures are 3 (7, 0, and 1).
- For the width (12 m), the significant figures are 2 (1 and 2).

### Step 3: Calculate the area
The area \( A \) of the rectangle is calculated using the formula:
\[ A = \text{Length} \times \text{Width} \]
Substituting the values:
\[ A = 7.01 \, \text{m} \times 12 \, \text{m} \]
\[ A = 84.12 \, \text{m}^2 \]

### Step 4: Apply the rules of significant figures
When multiplying, the result should have the same number of significant figures as the measurement with the least significant figures. Here, the width (12 m) has 2 significant figures, which is less than the 3 significant figures of the length (7.01 m).

### Step 5: Round the area to the correct number of significant figures
The calculated area is 84.12 m². Since we need to round this to 2 significant figures (due to the width), we look at the first two digits:
- The first two digits are 84. The next digit (1) does not affect rounding.
Thus, the area rounded to 2 significant figures is:
\[ A = 84 \, \text{m}^2 \]

### Final Answer
The area of the rectangle, taking significant figures into account, is:
\[ \boxed{84 \, \text{m}^2} \]

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