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
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- sat geometry review pdf
- mcdougal littell geometry book answers
- sat geometry practice worksheets
- mcdougal littell geometry practice answers
- geometry sat questions pdf
- sat geometry practice pdf
- geometry calculator online
- 6th grade geometry project
- 7th grade geometry project
- mcdougal littell geometry test answers
- mcdougal littell geometry workbook pdf
- free 10th grade geometry worksheets