The answer is 96√3 (√ is the root sign), which is definitely correct.

The circumference of a regular hexagon is 48, so each side is 8. You connect the two vertices of the diagonal and find that it has become six equilateral triangles, each with a side length of 8. In other words, you can find the area of each triangle and multiply it by 6 to get the area of a regular hexagon.

So how do you find the area of an equilateral triangle? You know, bottom × height ÷2. Then you make a height based on 8, and then you can work out the height. If you look for a right triangle, then the right side of a line is 4 and the hypotenuse is 8, then according to Pythagorean theorem (sum of squares on the right side = square of hypotenuse), you can find that the height is 4√3, and then use 8×4√3÷2= 16√3.

The final area is 16√3×6=96√3.

Answer over. Haha, it's more detailed! !

Finally, I wish you success in your studies and happy holidays!