CONCAVE OR CONVEX POLYGON CLASSIFICATION

Convex polygon :

A convex polygon is a polygon with all interior angles less than 180^º and vertices are pointed outwards.

Concave polygon :

A concave polygon is a polygon that has at least one interior angle greater than 180 degrees. It must have at least four sides.

State if each polygon is concave or convex.

Problem 1 :

Solution :

Concave polygon :

One or more diagonals are outside. A polygon has at least one angle that measures more than 180 degrees, which is called a concave polygon.

From the picture, one of the interior angle measure is more than 180 and one of the diagonal we can draw outside.

In the above diagram, the polygon shown is a concave polygon.

Problem 2 :

Solution :

Convex polygon : All diagonals are inside.

A convex polygon has all its interior angles less than 180 degrees.

In the above diagram, the polygon shown is a convex polygon.

Problem 3 :

Solution :

Convex polygon : All diagonals are inside.

A convex polygon has all its interior angles less than 180 degrees. So, it is convex polygon.

Problem 4 :

Solution :

Concave polygon : One or more diagonals are outside.

A polygon has at least one angle that measures more than 180 degrees, which is called a concave polygon.

In the above diagram, the polygon shown is a concave polygon.

State if each polygon is regular or not.

Problem 5 :

Solution :

By observing the figure, It is a irregular polygon.

Because, irregular polygon does not have all its sides equal.

Problem 6 :

Solution :

By observing the figure, seems all sides are equal. Then, it is a regular polygon.

Problem 7 :

Solution :

By observing the figure, all 8 sides are equal. So, it is regular polygon and name of the polygon is heptagon.

Problem 8 :

Solution :

By observing the figure, seems all sides are equal. Then, it is a regular polygon. The name of the polygon is pentagon.

Problem 9 :

Solution :

By observing the figure, since all sides are equal. So, It is a regular polygon. The name of the polygon is hexagon.

Problem 10 :

Solution :

By observing the figure, the sides are not equal. So, it is irregular polygon.