Page 179 - ICSE Math 8

Concave polygon (Fig. 16.7) is a simple polygon, that is not convex.
• It has at least one interior angle greater than 180º, i.e., it has an indentation.

• It is always possible to locate two points of a concave polygon so that the segment connecting them is not
wholly contained in its interior.

Fig. 16.7

Point to remember

If not mentioned, a polygon in geometry is considered to be a convex polygon.

Classification of Polygons
Polygons are of different types based on the number of sides. The number of sides is equal to the number of
vertices and angles.
Table 16.1

No. of sides Classification Sum of No. of sides Classification Sum of
or vertices interior angles or vertices interior angles
Octagon
Triangle
I
II
1,080°
3 180° 8 III IV (6 × 180°)
I
V
VI

Quadrilateral Nonagon
I
360° II 1,260°
4 I 9 III IV
(2 × 180°) (7 × 180°)
II V VI
VII

Pentagon Decagon
I
I 540° II
5 III 1,440°
II (3 × 180°) 10 IV V (8 × 180°)
III VI
VII
VIII
Hexagon n n-gon (n –2) × 180°
720°
6 I II IV (4 × 180°)
III

Heptagon

I 900°
7 II
III (5 × 180°)
IV V

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