Convex Polygon: Definition, Properties and Solved Examples

Convex Polygon: A convex polygon is one whose internal angles are all less than or equal to 180 degrees. It’s a polygon with a convex set of internal angles and no line segments between the points. It is a two-dimensional figure made up of angles and line segments. The convex polygon’s line segments are pointing away from the centre.

In order to grasp the geometrical forms for mathematical reasons, students study the shape of convex polygons in their basic schools. Allow them to answer math problems correctly as well. For a better understanding, read the Convex Polygon Definition Class 8 Maths Chapter 3. In this article, we have covered all there is to know about convex polygons. Continue reading to learn more about the definition of convex polygon, and its features and applications.

Definition Of Convex Polygon

Convex Polygon Definition: Convex Polygons are the line segments that are present away from the center. The interior angles of convex polygon measure up to less than or equal to 180 degrees. These are opposite to the concave polygons. For example, a triangle is the most important convex polygon.

Properties Of Convex Polygon

Some of the properties of the convex polygon are given below:

The interior angles are less than or equal to 180 degrees.
The diagonals are present inside the polygon.
The area of a polygon is calculated by dividing and adding the triangles of each polygon.

Download NCERT Solution for Class 8 Maths Chapter 3 PDF

What Is Convex Polygon With Example?

Some of the convex polygon examples are as mentioned below:

Example 1: What can you say about the angle sum of a convex polygon with a number of sides?
(a) 7
(b) 8
(c) 10
(d) n
Solution: The angle sum of a polygon having side n = (n – 2) × 180°
a) 7
Here, n = 7
Thus, angle sum = (7-2)×180° = 5×180° = 900°
b) 8
Here, n = 8
Thus, angle sum = (8-2)×180° = 6×180° = 1080°
c) 10
Here, n = 10
Thus, angle sum = (10-2)×180° = 8×180° = 1440°
d) n
Here, n = n
Thus, angle sum = (n-2)×180°

Example 2: Find the angle measures ? in the following figures:

Solution: Since there are 5 sides.

Therefore, n = 5.

We know that Angle sum of a polygon = (n − 2) × 180 °

= (5 − 2) × 180 ° = 3 × 180 ° = 540 °

∴ ? + ? + ? + ? + ? = 540 ° (Angle sum property)

⇒ 5? = 540 °

⇒ ? = 108 °

Hence each interior angle of the given polygon is 108 °.

FAQs On Convex Polygon

The frequently asked questions on convex polygon are given below:

Q. What is a convex polygon?
A. Convex polygon is defined as a polygon with all its interior angles less than or equal to 180 degree.

Q. What are the properties of a convex polygon?
A. The properties of a convex polygon are given below:
1. The interior angles are less than or equal to 180 degrees.
2. The diagonals are present inside the polygon.
3. The area of the polygon is calculated by dividing and adding the triangles of each polygon.

Q. What is the shape of the convex polygon?
A. It’s possible for a convex polygon to be regular or irregular. It’s a closed polygon with less than 180 degrees of inner angles. There are no vertices of a convex polygon pointing inside.

Q. State a few examples of the convex polygon?
A. Convex polygons include the kite, the Pentagon, the Hexagon, and the Heptagon, among others.

Q. Convex polygon has how many sides?
A. A closed-form with no vertices pointing inward is called a convex polygon. When a line crosses a convex polygon, it only touches two of the polygon’s sides. Convex polygons include pentagons, hexagons, and other shapes with vertices pointing away from the centre.

Now we have provided detailed information on the convex polygon in this article. You can solve the Convex Polygon Definition Class 8 practice questions on Embibe for Mathematics and Science. You can also take CBSE Class 8 Mock Tests for these subjects. These will be of great help to you.

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