Post on 11-Aug-2020
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Polygons - Part #2Regular Polygons
Regular Polygons
Recall:
Regular polygons are polygons that have congruent sides and congruent angles
Irregular polygons are polygons that have either: different side lengths, different angle measurements, or both
Common PolygonsName Number of Sides Diagram
Triangle 33
Quadrilateral 4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
Properties
Central Angle
Interior Angle
Exterior Angle
Measure of Interior AnglesWe can use a formula to find the measure of an interior angle of a regular polygon.
Formula: Measure of an Interior Angle
M = 180 (n-2)
———————n
Where n = the number of sides
ExampleFind the measure of an interior angle in a hexagon
ExampleFind the measure of an interior angle in a nonagon
ExampleFind the measure of an interior angle in a 12 sided regular polygon
Sum of Interior AnglesWe can use a formula to find the sum of the interior angles of a regular polygon.
Formula: Sum of the Interior Angles
S = 180 (n-2)
Where n = the number of sides
ExampleFind the sum of the interior angles of a hexagon
ExampleFind the sum of the interior angles in an octagon
ExampleThe sum of the interior angles of a polygon is 900°. Determine how many sides this polygon has.
Measure of the Central AngleWe can also determine the measure of the central angles in a regular polygon
The central angle is the angle made at the centre of a polygon by any two adjacent vertices of the polygon
Central Angle
Radius
Note: All central angles would add up to 360° (a full circle) so the measure of the central angle is 360 divided by the number of sides.
Formula: Measure of the Central Angle
Measure of the Central Angle
C = 360
———————n
Where n = the number of sides
ExampleWhat is the measure of the central angle in a hexagon?
ExampleWhat is the measure of the central angle in a heptagon?
Determining the DiagonalsDiagonals are straight lines that extend from one vertex to another
You can have multiple diagonals per vertex
Example:
We can also determine the number of diagonals in a regular polygon by using a formula
Determining the Diagonals
Formula: Determine the Number of Diagonals
D = n (n - 3)
———————2
Where n = the number of sides
ExampleDetermine the number of diagonals in a regular pentagon
ExampleDetermine the number of diagonals in a regular octagon