A polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain or circuit. These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices (singular: vertex) or corners.
A regular polygon is a polygon with all its sides and all its interior angles equal. All vertices of a regular polygon lie on a circle whose center is the center of the polygon.
Each side of a regular polygon subtends an angle Θ at the center given by
Also, the interior angle of a regular polygon is given by
Therefore, sum of all angles of a regular polygon(n-sided convex polygon) =
A regular hexagon
A regular hexagon is a closed figure with six equal sides. If we join each vertex to the center of the hexagon, we get 6 equilateral triangles. Therefore, if the side of the hexagon is a each equilateral triangle has a side a. Hence, the area of the regular hexagon is 6 x (√3/4)a2 .
A regular octagon
A regular octagon is a closed figure with eight equal sides. If we join each vertex to the center of the hexagon, we get 8 isosceles triangles.
Sum of all angles of a regular octagon(8-sided convex polygon) =
Measure of internal angles of an octagon =