The side and the radius of a regular hexagon are congruent therefore 6 times 12 is 72. The reason the radius and side are the same is that the radius bisects the angle and it is 120. 60 degree angles are part of an equilateral triangle.
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If it is a regular 6 sided hexagon then its perimeter is 6 times 12 = 72 inches
The perimeter of a hexagon with an apothem of 12 is 83.14
12 meters, you said.
If the perimeter of the hexagon is 72, then each side of the hexagon is 72/6 = 12. Therefore, one side of the square is also 12, since the hexagon and the square share a side, so the area of the square is 12 x 12 = 144 cm.
The area of a hexagon with a perimeter of 12 units is about 10.4 units2