11.4(b) Areas of Regular Polygons and Composite Figures ...

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.


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)


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.


Example #1

Find the area of a regular octagon with an apothem of 24 cm.


Example #2

Find the area of a regular hexagon with a perimeter of 72 in.


Example #3

Find the area of a square with a radius of 8 cm.


Example #4

Find the area of an equilateral triangle with an apothem of 3.3 m.


Example #5 (Practice Book #2)

Find the area of the regular polygon.


Example #6

Find the area of a regular hexagon with a radius of 26 m.


18

18

Find the shaded area of the figure.

11.4(b) Areas of Regular Polygons and Composite Figures ...

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