## All four sides are equal in length

### When all four sides of a polygon are equal in length, we refer to it as a regular polygon

When all four sides of a polygon are equal in length, we refer to it as a regular polygon. A regular polygon has congruent (equal) sides and congruent angles.

Some common examples of regular polygons include squares, equilateral triangles, and regular hexagons. In a square, all four sides are equal in length, and each angle is a right angle (90 degrees). Similarly, in an equilateral triangle, all three sides are equal in length, and each angle measures 60 degrees. In a regular hexagon, all six sides are equal in length.

Regular polygons have a number of interesting properties. For instance:

– The sum of the interior angles of a regular polygon can be found using the formula (n-2) * 180 degrees, where n represents the number of sides. For example, a regular pentagon (5 sides) has interior angle sum of (5-2) * 180 = 540 degrees.

– The measure of each interior angle in a regular polygon can be calculated using the formula (n-2) * 180 / n degrees. For example, in a regular heptagon (7 sides), each interior angle measures (7-2) * 180 / 7 ≈ 128.6 degrees.

– The measure of each exterior angle in a regular polygon is equal to 360 degrees divided by the number of sides. For example, in a regular decagon (10 sides), each exterior angle measures 360 / 10 = 36 degrees.

– The diagonals (lines connecting non-adjacent vertices) of a regular polygon are congruent and intersect at equal angles.

Understanding the concept of regular polygons and their properties is essential in various areas of geometry, architecture, and engineering.

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