Geometry



Geometry

Notes: Section 11.2 Area of Regular Polygons

Goals:

1. Find the area of a equilateral triangle

2. Define apothem and find its length

3. Use the apothem to find the area of a regular polygon

Review:

30-60-90 Triangle Right Triangle Trigonometry Area of a Triangle

SOH – CAH – TOA [pic]

Area of an Equilateral Triangle:

OR

Ex 1) Find the area of an equilateral triangle Ex 2) Find the area of an equilateral triangle

with side length of 8. with side length of 10

Ex 3) The area of an equilateral triangle is 15. Find the length of the sides.

**Skip slides 16 – 18**

Segments in a Regular Polygon:

The ______________________ distance from the ________________ of a regular polygon to one of its __________ is called the __________or __________________ It is the same as the ___________ of a circle inscribed in the polygon.

**OMIT SLIDES 21-25**

Area of a Regular Polygon:

Example:

1. Draw a radius and the apothem in the regular hexagon.

2. What kind of triangle is formed? ________________

3. What’s the length of the segment marked x? __________

4. What is r? ___________

5. What is a? ___________

6. What is the perimeter? __________

7. Now let’s find the Area…

A =_______________

A = ______________

**Skip slides 30 – 32**

If a regular polygon is anything other than an equilateral triangle, a square, or a hexagon,

45º-45º-90º 30º-60º-90º

then finding the apothem and the radius may be a little more challenging (but not impossible).

A Harder Example…

Find the Area of a Regular Pentagon.

➢ Understand where 36º came from…

Apothem = ____________ Perimeter = _____________

**If we have an angle and 1 side length

and need another side length,

A = [pic] (_______)(_______) THINK TRIG!(

Which trig function can be used to find x?

___________________

___________________

___________________

Harder Example #2:

Find the area of a regular octagon if the length of a side is 10.

> Find the measure of the Central Angle [pic] _________

> Draw the central angle and the apothem…the apothem will

divide the central angle and side in _________

> Find the measure of the angle _____ and the side length ______

> Apothem [pic] _______________

(TRIG()

> Perimeter = _______________

>

**Skip slide 50**

Should we add more examples at the end (from last year’s notes).

More Examples: All figures are regular.

1) 2)

7

3) 4)

12

20

5) What is the area of a regular triangle with apothem of 5?

6) Find the area of a regular hexagon with apothem [pic].

[pic]

-----------------------

Adjacent

Leg

Opposite

Leg

Hypotenuse

30º

60º

a

[pic]

2a

Base(b)

height(h)

A=[pic]

A=[pic]

s

s

s

___________

______

_________

A=[pic]

a = apothem p = perimeter

A=[pic]

6

36º

x _______

(Opposite Leg)

(Adjacent

Leg)

s _______

Area = ______________

10

_____

____

___

HWK:

WS 11.2

Area [pic] ________________

A

12

9.6

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