## Exterior of a polygon

### The exterior of a polygon refers to the region of the plane that lies outside the boundary of the polygon

The exterior of a polygon refers to the region of the plane that lies outside the boundary of the polygon. In other words, it is the space surrounding the polygon, excluding the interior and the edges of the polygon.

To visualize the exterior of a polygon, imagine drawing the boundary of the polygon with a pen, and then moving the pen away from the polygon without touching any of its edges or interior. The area of the plane where the pen is located outside the polygon is considered the exterior.

The exterior of a polygon has certain characteristics that can be helpful to understand. Firstly, any point in the exterior of a polygon is equidistant to at least one of the polygon’s sides. This means that the distance from any point in the exterior to the nearest side of the polygon is the same for every point.

Additionally, the exterior of a polygon is an open set, which means that it does not include any of its boundary points. For example, if the polygon has a corner or vertex, that point is not considered part of the exterior, but rather part of the boundary or interior.

Knowing the concept of the exterior of a polygon is useful in various applications of geometry and mathematics, including calculating areas, understanding convexity, and determining the properties of shapes and figures in relation to their surroundings.

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