It is reasonable, and can be done with a simple formula A = N * s * a / 2 for a regular convex polygon with N sides of length s. a is the shortest distance from the center point to one of the sides, known as the apothem. This formula can be viewed as first dividing the regular convex polygon into N identical triangles by connecting its center to its vertices. The area of each triangle is s * a / 2, where s is the base and a is the height. The total area of the triangles is N * s * a / 2.
Within each triangle, If we draw a perpendicular line from the center of the polygon to the base, we get two identical right triangles. The angle with the polygon's center as the vertex is 180°/N, and the length of the side opposite to it is s / 2. Therefore, the side adjacent to it, or the apothem, is s * cot(180°/N) / 2, and the area of the regular convex polygon A = N * s^2 * cot(180°/N) / 4.
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