POLYGONS

A polygon is a plane figure that meets the following conditions.

1. It has to be a closed figure. That is, each side intersects exactly two other sides, one at each end point.

2.  Each side of the figure must be a straight line.

Each endpoint of a side is a vertex of the polygon. The plural of vertex is vertices. We can name a polygon by listing its vertices consecutively. For instance, PQRST or RQPTS are two correct names for the polygon above.

Regular Polygon :

If a polygon is equilateral (all sides are equal in length) and equiangular (all interior angle measures would be equal), then it is regular polygon.

Concave Polygon :

In a polygon, when extended, some of the sides intersect the interior, then the polygon is concave.

Convex Polygon :

In a polygon, when extended, none of the sides intersect the interior, then the polygon is convex.

Note :

The minimum number of sides required to form a polygon is 3. No polygon can be formed with less than 3 sides.

Number of Sides and Names of Polygons

Solved Questions

Question 1 :

State whether the figure given below is a polygon or not. Explain why.

Answer :

Yes, it is a polygon

Because, it is a closed a figure and all the sides of the polygon are straight lines.

Question 2 :

State whether the figure given below is a polygon or not. Explain why.

Answer :

Yes, it is a polygon

Because, it is a closed a figure and all the sides of the polygon are straight lines.

Question 3 :

State whether the figure given below is a polygon or not. Explain why.

Answer :

No, it is not a polygon

Because, one of the sides is not a straight line.

Question 4 :

State whether the figure given below is a polygon or not. Explain why.

Answer :

No, it is not a polygon

Because, it is not a closed figure.

Question 5 :

State whether the figure given below is a polygon or not. Explain why.

Answer :

No, it is not a polygon

Because, some of its sides intersect more than two sides.

Question 6 :

Identify the polygon and state whether it is convex or concave.

Answer :

The polygon has 8 sides, so it is an octagon.

When extended, some of the sides intersect the interior, so the polygon is concave.

It has been illustrated in the diagram shown below.

Question 7 :

Identify the polygon and state whether it is convex or concave.

Answer :

The polygon has 5 sides, so it is an pentagon.

When extended, none of the sides intersect the interior, so the polygon is convex.

It has been illustrated in the diagram shown below.

Question 8 :

Decide whether the polygon is regular.

Answer :

All the sides of the polygon above are equal in length.

But, all the angles do not have equal measure.

So, it is not a regular polygon.

Question 9 :

Decide whether the polygon is regular.

Answer :

All the sides of the polygon above are equal in length.

And also, all the angles have equal measure.

So, it is a regular polygon.

Question 10 :

Decide whether the polygon is regular.

Answer :

All the sides of the polygon above are equal in length.

But, all the angles do not have equal measure.

So, it is not a regular polygon.

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