If it is a regular polygon--meaning that all the sides are congruent and all the angles are congruent, then the formula for area of the polygon is A=1/2 ap Here a represents the apothem, which is the distance from the center of the polygon to the midpoint of one side. p represents the perimeter of the polygon found by multiplying one side length by the number of sides. If you only know one variable such as side length, you can find the perimeter and you can find the apothem using trigonomety.
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The lengths of sides of any polygon with more than 3 sides do not provide enough information to calculate the area. For example, a square can be skewed into a rhombus which can then be made so thin that its area is [asymptotically] equal to 0.
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 perimeter of a polygon is the sum of the length of each of its sides. If the polygon is a regular polygon the you can calculate the perimeter as [number of sides] *[the length of one side]
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.