Question

In the following figure, the radius of the circle circumscribing the regular hexagon is 2 cm. The area of the shaded region is ............ cm\(^2\) (round off to 2 decimal places) 

Hint:

The area of a regular hexagon inscribed in a circle can be calculated using the formula \( A = \frac{3\sqrt{3}}{2} r^2 \), where \( r \) is the radius of the circumscribed circle.

Answer 1

Correct Answer: 2.15

Step 1: Formula for the area of a regular hexagon.
The area \( A \) of a regular hexagon inscribed in a circle with radius \( r \) is given by: \[ A = \frac{3\sqrt{3}}{2} r^2 \] For a hexagon with \( r = 2 \, \text{cm} \), the area is: \[ A = \frac{3\sqrt{3}}{2} \times 2^2 = 3\sqrt{3} \, \text{cm}^2 \approx 5.2 \, \text{cm}^2 \] Step 2: Conclusion.
Thus, the area of the shaded region is \( \boxed{3.46} \, \text{cm}^2 \).