If it's a regular polygon, and you know the length of the perpendicular from the center to the middle of a side, and the length of a side, A = LNS, where L is the length of the perpendicular, N is the number of sides, and S is the number of sides.
See the link for a more detailed explanation of various ways to compute the area of regular polygons.
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No, a line is not a polygon. A polygon is a closed plane area bounded by straight sides. A line, by itself, does not contain an area.
A polygon has lengths, angles, a perimeter and area.
The area of a polygon is the two-dimensional set of all points surrounded by the sides of the polygon. If you're looking for an equation, it varies based on the number of sides and the shape of the polygon.
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Area of regular polygon: 0.5*apothem*perimeter