Question

The length of each side of a regular octagon is 1 meter. The area of the octagon in m² is ............ (decimal digits up to 2 places)

Hint:

To calculate the area of a regular octagon, use the formula \( A = 2(1 + \sqrt{2})a^2 \), where \( a \) is the side length.

Answer 1

Correct Answer: 4.8

Step 1: Formula for the area of a regular octagon.
The area \( A \) of a regular octagon can be calculated using the formula: \[ A = 2(1 + \sqrt{2})a^2, \] where \( a \) is the length of a side of the octagon.

Step 2: Substitute the value of \( a \).
Since \( a = 1 \) meter, we substitute this value into the formula: \[ A = 2(1 + \sqrt{2}) \times 1^2 = 2(1 + 1.414) = 2 \times 2.414 = 4.828 \, \text{m}^2. \]

Step 3: Conclusion.
The area of the octagon is approximately 2.0 m².