Polygons

In this post, i will teach you how to calculate a topic in mathematics called POLYGON. It is well known that, a polygon is plane shape with three or more sides, in which none of intersects each other, but all form an enclosed geometric figure. A polygon is named according to the number of sides it has.

Classification Of Polygons

There are different types of polygon, and they are:

(a) Convex Polygon

(b) Re- entrant Polygon

(c) Regular  Polygon

(a) Convex Polygon: In this type of polygon, each interior angle is less than  180 degree.An example is hexagon.

(b) Re- entrant Polygon :A convex polygon is a type of polygon with one or more of its interior angles reflex,i.e it is greater than 180 degree.

(c) Regular  Polygon:A regular polygon is a type shape  in which all its sides and angles are equal.

Now, i will mention some eaxmples of polygon names, number sides and number of angles.

NAME            NUMBER OF SIDES         NUMBER OF TRIANGLES

Triange             3                          1

Quadrilateral       4                          2

Pentagon            5                          3

Hexagon             6                          4

Heptagon            7                          5

Octagon             8                          6

Nonagon             9                          7

Decagon             10                         8

Undecagon           11                         9

Dodecagon           12                         10

Tridecagon          13                         11

etc

In a polygon, a convex polygon VWXYZ ....... with n sides (where n is the total sides)

To prove V + W + Y + Z ----(2n - 4) right angles.

Example 1

What is the sum of the interior angles of a duodecagon polygon?

Solution

A dodecagon polygon has 12 sides ; n = 12

Sum of the interior angles = (2n - 4)right angle

= ( 2 x 12 - 4) x 90 degree

= (24 - 4) x 90

= 20 x 90

= 1800 degree

Based on the explanation about any angle less tha 180, such solution must be 90.That means any angle less that 90 shuld go with formula

(2n - 4) x 90

Example 2

If the interior angles of a quadrilateral are x , (2x + 5) , (x + 15) and (2x + 10) degrees, find x.

Solution 

We all know that a type of angle called quadrilateral has 4 sides (rectangle and square).

x + (2x + 5) + (x + 15)  + (2x + 10) = 360 degree

x + 2x + 5 + x + 15  + 2x + 10 = 360

6x + 30 = 360

Subtract 30 fro both sides.

6x + 30 - 30 = 360 - 30

6x = 330

Divide both sides by 6 not (6x)

   6x      330

------- = ------ 

   6        6

x = 55 degree

Example 3

One of the angles of an octagon is 156 degree.Find the values of the other angles, if they are equal.

Solution

An octagon has 8 sides.Let each of the remaining 7 angles be x.

7x + 156 = (2n - 6) right angles.

        = (2 x 8 - 4) x 90

        = (16 - 4)  x 90

        = 12 x 90 

        = 1080

7x + 156 = 1080

Subtract 156 from both sides

7x + 156 - 156 = 1080 - 156

7x = 924

Divide both sides by 7( not 7x).

  7x        924

------- = ------- 

  7         7

x = 132 degree

More eamples

The sum of the interior angles of a polygon of n sides is 900 degree.Find the value of n.

L et n sides is a ply gon with 7 sides.

Heptagon = 7

=(2n - 4) right angles

= ( 2 x 7 - 4) x 90

= ( 14 - 4) x 90

= 10 x 90

= 90

ACtivities 1

Calculate the sum of the following interior angles.

(a) 5- sides

(b) 15 - sides

(c)20 sides

ACtivities 2

(a) A regular polygon has angle of size 150 each. many sides does the polygon have?

(b) If the exterior angles of a pentagon are x, (x + 5),(x + 10), (x + 15) and (x + 20), find x