**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.

3 4 5 6 7 8 9 10 n |
Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon n-gon |

**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.

After having gone through the stuff given above, we hope that the students would have understood, "Polygons".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

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