Polygons always give shiver to most students but you don’t need to be afraid of it. Polygon is no scary topic, in fact it is a really interesting topic and you can master it with some basic points and practice.
Let us understand what polygons are and what its concepts are:
Any two-dimensional figure made up of three or more straight sides are known as polygons. The naming of the polygons is done according to the number of sides they are made of.
Name of Polygon |
Number of sides |
Triangle | 3 |
Quadrilateral | 4 |
Pentagon | 5 |
Hexagon | 6 |
Heptagon | 7 |
Octagon | 8 |
Nonagon | 9 |
Decagon | 10 |
Do-decagon | 12 |
n-gon | n |
Properties of Polygon
Some properties that all polygons follow irrespective of the number of sides they have.
- The sum of all the interior angles of a polygon having n- number of sides (n – 2)×180°. For example, the summation of the interior angles of a do-decagon will be (12 – 2) × 180°= 10 × (180°) = 1800°.
- Any polygon that has equal interior angles and equal side is known as a regular polygon.
- The perimeter of a polygon = Summation of all the sides of the polygon
- The total sum of the exterior angles of any polygon = 360°.
- The area of a polygon = The region bounded by the polygon. Each polygon figure has different formulas specified for calculating their area.
Characteristics of Polygons
Triangles: This is the simplest form of polygon having only three sides. Properties of triangle:
- The summation of the two sides of a triangle is always greater than the third side. Similarly, the difference of two sides is less than the third side.
- The greater is the angle of a triangle, the greater will be its corresponding side.
- The sum of the internal angles of a triangle is always supplementary.
Quadrilaterals: Quadrilaterals are made up of four straight sides.
- There are mainly six types of quadrilaterals, namely; square, rectangle, kite, parallelogram, trapezium and rhombus.
- Sum of internal angles as well external angle of a quadrilateral is always equal to 360o.
Pentagon: Five straight sides together make up a pentagon
- The summation of the internal side of a pentagon is equal to 540o
- The angle made at the center of a pentagon formed by each side = 360o ÷5 = 72o.
- Every individual angle of a pentagon = 108o
A standard formula can be used to describe the features of a polygon. Usually the polygons tested in GRE are triangles and quadrilaterals. The quadrilaterals that are highly liked by GRE are: parallelograms, square, rectangle and kites.
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