Question

A regular octagon ABCDEFGH has sides of length 6 cm each. Then the area, in sq. cm, of the square ACEG is

• A. \({36(1 + \sqrt{2})}\)
• B. \({72(2 + \sqrt{2})}\)
• C. \({72(1 + \sqrt{2})}\)
• D. \({36(2 + \sqrt{2})}\)

Answer 1

The Correct Option is D

The area of square $ACEG$ can be calculated using geometry of regular polygons. The side length of the octagon is given as 6 cm, and using geometric properties of a regular octagon, we calculate the area of the square formed by the diagonals. Using trigonometric and geometric formulas, the area of square $ACEG$ is found to be:
\(\boxed{36(2 + \sqrt{2})}\)
Thus, the correct answer is Option (4).