Some basic geometric formulas for regular polygon. A regular polygon is one which has all the sides are equal

The area of a regular polygon is always = 1/2 (apotherm) x (perimeter) : Refer to the illustration 2nd Image

If n = Numbers of side of the polygon , S = Length of the side of the polygon, r = radius of the circumcircle, a = apotherm ) refer to the second image for illustration

1.** Measure of the interior angle = [(n-2)/n] x 180 degrees**

2. **Sum of the interior angles = (n-2) x 180 degrees**

3. **The number of diagonals in a polygon = 1/2 [n x (n-3)]**

4. **The number of triangles (when you draw all the diagonals from one vertex) in a polygon = (n – 2)**

5. **Area of a regular polygon = (1/2) n sin(360°/n) s ^{2}**

6. Interior Angle + Exterior Angles = 180^{o}

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