9 Polygons - Concave Convex

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Polygons ndash An introduction

Definition of a Polygon

A closed plane figure made up of several line segments that are joined together where the sides

do not cross each other and every two adjacent sides meet at a vertex The lines that are joined

together form a closed path called a polygon

Figure 1 Polygon Parts

Figure 1 above shows the parts that make up a polygon They are

1- Side each line segment that make ups the polygon is called a side

2- Vertex the point where any two sides meet

3- Interior Angle Angle formed by two adjacent sides inside the polygon (the green angle in

Figure 1)

4- Exterior Angle Angle formed by two adjacent sides outside the polygon (the blue angle

in Figure 1)




5- Diagonal a line that connects two vertices together (other than a side)

Polygons are named based on how many sides they have Below is a table that lists some of the

most common polygons

Table 1 Common Polygons

Name Sides Angles

Triangle 3 3

Quadrilateral 4 4

Pentagon 5 5

Hexagon 6 6

Heptagon 7 7

Octagon 8 8Nonagon 9 9

Decagon 10 10

Types of Polygons

1- Equiangular all angles are equal Example Equilateral triangle rectangle

2- Equilateral all sides are the same length Example Square equilateral triangle

3- Regular all angles are equal and all sides are the same length Regular polygons are both

equiangular and equilateral Example Square equilateral triangle

4- Convex every interior angle is less than 180deg and a straight line drawn through such a

polygon crosses at most two sides

Figure 2 Convex polygon




5- Concave at least one interior angle is greater than 180deg and it is possible to draw at least

one straight line that crosses more than two sides

Figure 3 Concave polygon

6- Cyclic all corners lie on a single circle

Figure 4 Cyclic Polygon

7- Tangential all sides of the polygon are tangent to an inscribed circle

Figure 5 Tangential polygon




8- Rectilinear a polygon whose sides meet at right angles Example square rectangle

Some Important Polygon Formulas

For a polygon with N sides and length of a side = X we have

1- Area of a regular polygon =

983139983151983156983080

983216

983081983084 ℎ 983139983151983156 983101

983086

2- Sum of the interior angles of a polygon = 983080 minus 983090983081 983089983096983088983216

3- The number of diagonals in a polygon =

983080 minus 983091983081

983092983085 The number of triangles (when you connect all the diagonals from one vertex to the

others) that can be drawn in a polygon = minus 983090




5- Diagonal a line that connects two vertices together (other than a side)

Polygons are named based on how many sides they have Below is a table that lists some of the

most common polygons

Table 1 Common Polygons

Name Sides Angles

Triangle 3 3

Quadrilateral 4 4

Pentagon 5 5

Hexagon 6 6

Heptagon 7 7

Octagon 8 8Nonagon 9 9

Decagon 10 10

Types of Polygons

1- Equiangular all angles are equal Example Equilateral triangle rectangle

2- Equilateral all sides are the same length Example Square equilateral triangle

3- Regular all angles are equal and all sides are the same length Regular polygons are both

equiangular and equilateral Example Square equilateral triangle

4- Convex every interior angle is less than 180deg and a straight line drawn through such a

polygon crosses at most two sides

Figure 2 Convex polygon


















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9 Polygons - Concave Convex

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