Today we will be covering a very important topic from the quantitative aptitude section that is – Polygon. These formulas will be helpful for your upcoming SSC & Railways Exams 2020. If you like it let us know.
Polygon
A closed figure in a plane with 3 or more sides and common endpoints.
Polygons are two-dimensional geometric figures with these characteristics:
- They are made of straight-line segments.
- Each segment touches exactly two other segments, one at each of its endpoints.
- They are closed they--divide the plane into two distinct regions, one "inside" and the other "outside" the polygon.
These shapes are polygons:
- These shapes are not polygons:
Types of polygons based on the number of sides
- Quadrilateral: 4 sides
- Pentagon: 5 sides
- Hexagon: 6 sides
- Heptagon: 7 sides
- Octagon: 8 sides
- Nonagon: 9 sides
- Decagon: 10 sides
- N-gon: n sides
Polygons with more than 10 sides are not usually given special names. A polygon with 11 sides is described as an 11-gon, a polygon with 12 sides as a 12-gon, and so on. Each of the polygons below is a 17-gon.
- A regular polygon is a convex polygon with all sides and angles congruent.
Convex pentagon Concave pentagon
A. Area of a regular polygon =
B. Area of a Hexagon = 
C. Area of an Octagon = 
Example 1: Find the area of a regular hexagon whose side measures 9 cm.
Solution:
Area of a regular hexagon=
Here, a = 9 cm
sq. cm = 210.4 sq. cm approx
Example 2: Find the nearest metre the side of a regular octagonal enclosure whose area is 1 hectare.
Solution:
Now, 
hectare
sq.m or, 
2071 sq. approx.
a=46 metres approx
- The sum of the angles of a triangle is 180o. What is the sum of the angles of a quadrilateral? Break polygon up into triangles to get formula:
Sum of angles = 180(n - 2)
- What is the sum of the angles of a pentagon? = (540)
- What is the sum of the angles of a nonagon? = (1260)
- If a pentagon is regular what is the measure of each interior angle?= (108)
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