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

Answer: (D)

${36(2 + \sqrt{2})}$

Answer 2

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).