# Polygons

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.

## Regular Polygons

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) = 180(n2)

Hexagon

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 .

Octagon

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) = 180(82)=1080o

Measure of internal angles of an octagon = 1080/8=135o

### Relevant exercises

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