Reasoning Formulas of Polygon in Quant section

Formulas of Polygon in Quant section

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

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 =

Example 1: Find the area of a regular hexagon whose side measures 9 cm.

Solution:

Area of a regular hexagon=

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:

sq.m    or,

2071 sq. approx..

a = 46 metres approx

• The sum of the angles of a triangle is 180^o. 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)