Final answer:
The area of a reduced hexagon by a scale factor of 1/3 is calculated by multiplying the original area by (1/3)².
Step-by-step explanation:
Understanding Scale Factor and Area
To determine the area of a reduced hexagon by a scale factor of 1/3, we first need to understand that when a figure is scaled down, its area changes by the square of the scale factor. If the original hexagon had an area of A, then the area of the reduced hexagon is A × (1/3)². Unfortunately, without knowing the original area, we cannot provide a numerical answer from the options given.
However, assuming the original area is 27 times that of the reduced area (since 3² = 9, and we must multiply the reduced area by 9 to get the original), let's check the options to see which when multiplied by 27 gives a perfect square, as an area of a hexagon should be. Only option b) 12 in² when multiplied by 27 (12×27=324) results in a perfect square of 18 squared. Thus, if we had an original hexagon and scaled it down by 1/3, the resulting area would be 1/9th of the original area.