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Interior and Exterior of a Closed Curve

Maths Talk
The interior region has
a boundary. Does the
exterior have a boundary? Discuss
with your friends.
Interior of the closed curve Exterior of the closed curve
The blue shaded part represents the interior and exterior of the closed curve respectively.

Polygons

A polygon is a simple closed curve formed by only line segments. In a polygon:
(a) no two line segments intersect except their end points.

(b) no two line segments with a common end points are coincident.

In the figures given below, the shapes shown in (a) and (b) are polygons, whereas those shown in
(c) and (d) are not polygons. In (c) and (d), the curves are closed but the lines intersect other than
end points.

(a) (b) (c) (d)
So, a polygon is defined as a closed figure formed by line segments such that no two line segments
intersect each other except at their end points.

A simplest polygon that can be drawn is a triangle. It is a 3-sided polygon. Thus, to draw a polygon
we need at least three line segments.

Example 2: Which points are:
A
(a) on the polygon. Q
F B
(b) in the interior of the polygon. Y
P X Z
(c) in the exterior of the polygon.
E C
Solution: (a) Point Z is on the polygon.

(b) Points X and Y are in the interior of the polygon. D
(c) Points P and Q are in the exterior of the polygon.

Knowledge Desk

Polygon is a combination of two Greek words ‘Polus + Gonia’, in which ‘Polus’ means many and ‘Gonia’
means corner or angle.

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