Question

How do you describe shapes that are not polygons, what are some examples?

Answer 1

Hint:
A polygon is any shape which has 3 or more sides where all sides are bounded forming a closed figure, number of angles are equal to number of sides and most importantly, no intersection or curved sides therein. If any of the above requirements are not met, the shape cannot be said to be a polygon.

Complete step by step solution:
“A polygon is any shape which has 3 or more sides where all sides are bounded forming a closed figure, number of angles are equal to number of sides and most importantly, no intersection or curved sides therein. If any of the above requirements are not met, the shape cannot be said to be a polygon”.
Let’s analyse the statements one by one and see which figures can be regarded as a polygon and which cannot.
1) A polygon is any shape which has 3 or more sides where all sides are bounded forming a closed figure

As for the first statement, a polygon must have 3 or more sides so if it has one side, it will be a line and as for two sides, it cannot form a closed figure also violating this statement. Also figures having more sides but not closed are not polygons. The above examples clarify the same.
2) Number of angles are equal to number of sides
This excludes all 3-dimensional figures and so they cannot be polygons because their number of angles can never be equal to the number of sides. As such, cubes, cuboids, cones etc. are all excluded.
3) No intersection or curved sides
This excludes shapes such as circles, arcs or other random shapes which possess curved sides. Also, it excludes shapes such as hourglass shape etc because of the intersections.

As such some shapes which are not polygons are all 3-D figures such as cubes, cuboids etc, shapes with curves such as circles etc, hourglass shapes which have intersecting lines and all of the shapes which don’t obey the aforesaid rules.

Note:
Always remember that when determining if a shape is a polygon or not, order of business must be to first find if it is a 2-D figure or not because only such figures can be polygons, next look for curves and unbound lines and if there are none then there is no need to match angles with sides.