## Concave polygons

### A concave polygon is a polygon that has at least one interior angle greater than 180 degrees

A concave polygon is a polygon that has at least one interior angle greater than 180 degrees. In other words, it is a polygon that “caves in” or has at least one “indentation” in its boundary. This is the opposite of a convex polygon, which has all of its interior angles less than 180 degrees.

To understand concave polygons, let’s look at an example. Consider a polygon with five sides. If all of the interior angles are less than 180 degrees, it is a convex pentagon. However, if one of the interior angles is greater than 180 degrees, it is a concave pentagon.

In a concave polygon, there is at least one “cut” or “dip” in the shape where the interior angle exceeds 180 degrees. This might create regions within the polygon where the angles “cave inwards” or “point towards the interior” rather than “point outwards” like in a convex polygon.

It is important to note that the vertices of a concave polygon are not necessarily all on the “outside” or “boundary” of the shape. Some vertices can be “inside” the polygon due to its concave nature. This is in contrast to convex polygons where all vertices are on the boundary.

The presence of concavities in a polygon can make certain calculations and properties more complex. For example, determining the area or calculating the perimeter of a concave polygon may require breaking it down into smaller, simpler components and summing their areas or perimeters.

In summary, a concave polygon is a polygon with at least one interior angle greater than 180 degrees, and it is characterized by “caving in” or having indentations in its boundary.

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