regular polygon
a polygon that is both equilateral and equiangular
A regular polygon is a two-dimensional shape with straight sides, where all sides have equal length and all angles between sides are equal. Each vertex of a regular polygon is equidistant from the center of the shape, making it symmetric around the center.
In order for a polygon to be regular, it must meet two criteria: all sides have the same length and all angles between sides are the same. The number of sides a regular polygon has is represented by ‘n’. Thus, a polygon with 3 sides (a triangle) is a regular polygon, as is a polygon with 4 sides (a square), and so on. The formula for finding the interior angle of a regular polygon is:
Interior angle = (n – 2) * 180 / n
This formula can be used to find the size of each interior angle for any regular polygon. For example, a regular hexagon has 6 sides, so using the formula above, we can find that each interior angle is equal to:
(6-2) * 180 / 6 = 120 degrees
The formula for finding the perimeter of a regular polygon is:
Perimeter = n * s
where ‘s’ represents the length of one side of the polygon. So, to find the perimeter of a regular hexagon with sides of length ‘5’, we would use:
Perimeter = 6 * 5 = 30
Therefore, the perimeter of a regular hexagon with sides of length 5 is 30 units.
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