GHLesson 114(b)_notes.notebook March 02, 2016
11.4(b) Areas of Regular Polygons and Composite Figures
Students will be able to . . .
• find areas of composite figures.
• find areas of regular polygons.
Review
What are the characteristics of a regular polygon?
All sides are congruent.
All interior angles are congruent.
GHLesson 114(b)_notes.notebook March 02, 2016
center to vertex of polygon
apothem (a) connects center to midpoint of a side; height of a triangle
Area of regular polygon
=Area of one triangle
Number of triangles
Area of one triangle = 1
2
length of one side of the polygon
n = Number of triangles or number of sides of the polygon
apothem
radius (r)
GHLesson 114(b)_notes.notebook March 02, 2016
Finding the area of a regular polygondon't know all of the necessary information.
1. Draw the isosceles triangle created by connecting the center to two consecutive vertices. Do NOT draw the entire polygon.
2. Find the area of the triangle (exact).
measure of vertex angle = 360/n
Draw the apothem (height of the triangle) creating 2 congruent right. Apothem bisects vertex angle.
Use trig or properties of a special right triangle to find the unknown lengths.
3. Find area of the regular polygon (exact and decimal).
To find the area of a regular polygon, need to know . . .
• apothem
• length of one side of the polygon
• number of sides of the polygon.
GHLesson 114(b)_notes.notebook March 02, 2016
Example #1
Find the area of a regular octagon with an apothem of 24 cm.
GHLesson 114(b)_notes.notebook March 02, 2016
Example #2
Find the area of a regular hexagon with a perimeter of 72 in.
GHLesson 114(b)_notes.notebook March 02, 2016
Example #3
Find the area of a square with a radius of 8 cm.
GHLesson 114(b)_notes.notebook March 02, 2016
Example #4
Find the area of an equilateral triangle with an apothem of 3.3 m.
GHLesson 114(b)_notes.notebook March 02, 2016
Example #5 (Practice Book #2)
Find the area of the regular polygon.
GHLesson 114(b)_notes.notebook March 02, 2016
Example #6
Find the area of a regular hexagon with a radius of 26 m.
GHLesson 114(b)_notes.notebook March 02, 2016
18
18
Find the shaded area of the figure.
![11.4 The Chain Rule. Composite Functions Definition: A function m is a composite of functions f and g if m(x) = f [g(x)] The domain of m is the set of.](https://static.documents.pub/doc/80x56/56649ed45503460f94be5543/114-the-chain-rule-composite-functions-definition-a-function-m-is-a-composite.jpg)
