Any side of the hexagon can be its base.
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6 A Regular Hexagon has six sides of equal length, and 6 equal angles.
They're referred to as hexagonal prisms. or a hexagonal pyramid.
The 7-faced solid is called a "hexagonal pyramid."
The question does not state that it is a regular hexagon and so you may not assume that it is. Therefore, there is no simple formula because a hexagon can have very many shapes. One method would be to pick a point in the plane of the hexagon and join it to all the vertices. This divides up the hexagon into triangles. Their areas can be calculated using base and height, or three sides, or two sides and included angle - whichever you like. Finally the areas of the triangles must be combined to get the area of the hexagon.
a hexagon has 6 sidesAn hexagon is a 6 sided polygon