Can a polygon have curved sides?

Answer 1

NO

A polygon is a closed, 2-dimensional (planar) shape made up of three or more straight line segments connected end to end to end.

By this definition, triangles, quadrilaterals and pentagons are all examples of polygons. Circles (etc.) are not, as they are not composed of (straight) line segments. Note that the shape can be convex (which we're used to) or concave, meaning that all the straight line segments may not lie along a "perimeter" but can "go inside" and "come back out" to form the shape.:

(For illustrations, see related link)

Regular versus Irregular PolygonsThe sides of a regular polygon are all equal. Also, the internal angles are equal to each other, whereas an irregular polygon's interior angles are unequal. Think of a Stop sign. That is a regular octagon. Any distortion of it -- changing the length of one side or increasing (decreasing) any of the angles would result in an irregular octagon.

A regular polygon is a convex plane shape with all of its sides the same length, and all its internal angles the same size. An irregular polygon will have unequal sides and angles, and can be either convex or concave. For example, regular polygons are equilateral triangles and squares, irregular polygons include 'scalene triangles', rhombi (angles differ), and rectangles (2 sides longer).

In a regular polygon, all the sides are congruent to each other. All the angles are congruent to each other. A regular triangle (also known as an equilateral triangle) has all of its sides measuring the same length and all three of its interior angles measure 60 degrees. So it is equilateral and equiangular.

A polygon with n sides is termed as regular only when each of its angles is given by (n-2)/n*180 and the ratio between any two sides is 1:1.

Examples of Regular Polygons

Equilateral triangle

Square

Examples of Irregular Polygon

Scalene triangle

Rectangle ("oblong")

Convex PolygonA convex polygon is a 3 or more sided shape where any straight, non-tangent line would intersect only two sides and only two points. A concave polygon has sides that, if extended as lines, would intersect a non-adjacent side.

(see examples at related link)