Page 79 - Start Up Mathematics_6

(ii) The points lying outside the closed curve are called its exterior.

(iii) The points lying on the curve constitute its boundary.
In the given figure, point ‘P’ lies in its interior, Q in its
exterior and R lies on its boundary. The interior of the P
curve together with its boundary is called its region. R Q

Let’s take a practical example. If Krish is playing cricket
in a playground having a closed boundary rope and Arushi
is watching him play from outside, then we say that Krish
is in the interior of the playground and Arushi is in its
exterior. The flags on the rope constitute its boundary.

Polygons

A simple closed figure made up of line segments only is called a polygon. In other words, a
polygon is a closed figure formed by straight lines joining only at their end points.
Let’s observe the following closed figures:

(i) (ii) (iii) (iv) (v) (vi)
Figures (i), (ii), and (iv) are examples of polygons. Figures (iii) and (v) are made up of line
segments and curves, hence they are not polygons. Figure (vi) is made up of line segments only,
but two of its sides are intersecting in the middle, hence it is also not a polygon.

Sides, vertices and diagonals of polygons
In the given figure, the polygon is made of 5 line segments AB, BC, CD, D
DE and EA. These line segments are called the sides of the polygon.
A, B, C, D and E are the vertices of the polygon. Its vertices taken in order, E C
i.e., ABCDE help us to name the polygon. A line segment joining any two
non-consecutive vertices is called a diagonal. In the given figure, AC and
AD are two of its diagonals. Can you find the other three? A B

Example 6: Classify the following curves as (i) open or (ii) closed.

(a) (b) (c) (d)
Solution: (a) Closed (b) Open (c) Closed (d) Open E D
Example 7: Draw any polygon and shade its interior. Is every F C

polygon closed?
Solution: Yes, every polygon is closed. A B

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