Assuming same side length, the the heptagon with 7 sides will have a greater area than a hexagon with 6 sides.
If the side lengths are not equal, then:
If the side of the hexagon is approx 1.183 times that of the heptagon then the areas are the same.
Thus when the side of the hexagon is less than ~1.183 times that of the heptagon it will have a smaller area; conversely, if the side of the hexagon is more than ~1.183 times that of the heptagon it will have a larger area.
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heptagon
Heptagon
Pentagon hexagon heptagon octagon
The answer is a Nonagon. Hope this helps!!
It has 1 more side