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```Elizabeth Pawelka
Geometric Probability
4/11/12
Geometry
Lesson Plans
Section 9-5: Trigonometry and Area
4/18/12
Pre-Quiz Warm-up (5 mins)
Find value of each variable to the nearest tenth.
 Check your sides with the Pythagorean Theorem.
 Check angles with Triangle Angle Sum Theorem/Complementary Angles
Ask for any questions on sections 9-1/9-2
Quiz on sections 9-1/9-2 (25 mins)
Post-Quiz Seat-work (15 mins)


“When a Ruler Isn’t Enough” worksheet
Reteaching 9-3: p. 109 # 1, 3, 4, 5
p.1
Elizabeth Pawelka
Geometric Probability
4/11/12
p.2
Homework Review (10 mins) – ask for any questions on homework
Homework (H)
 p. 484, #1 – 21, 23, 28, 33, 34
Homework (R)
 p. 484, #1 – 21, 23, 33
Statement of Objectives (5 mins)

The student will be able to use trigonometry to find area of polygons.
Teacher Input (25 mins)
Area of a regular polygon = ½ ap
Use trigonometry to find apothem:
p = 5 * 8 = 40cm
Find measure of central angle: 360/5 = 72
m∠XCY = ½ m∠XCZ = 36.
XY = ½ XZ = 4
tan(36) = 4/a
a = 4/tan(36)
a = 5.5
A = ½ (5.5)(40) = 110.11055
Find area of regular octagon with perimeter of 80.
Elizabeth Pawelka
Geometric Probability
4/11/12
side = 80/8 = 10
angle = ½(360/8) = 22.5
tan(22.5) = 5/a
a = 5/tan(22.5)
a = 12.1
A = ½(12.1)(80) = 482.8 in2
Find area of these regular polygons
p.3
Elizabeth Pawelka
have a, need perimeter: 2x(6)
tan(30) = x/6
x = 6 tan(30)
x = 3.46
p = 2(3.46)*6 = 41.57
A = ½(6)(41.57) = 124.71 cm2
Geometric Probability
4/11/12
p.4
p = 10 * 12 = 120
need a: central angle = 360/10 = 36
36/2 = 18
tan(18) = 6/a
a = 6/tan(18) = 18.466
A = ½(18.466)(120) = 1107.966 = 1108 cm2
Elizabeth Pawelka
Geometric Probability
Area of Triangles
What if you only had m∠A and lengths b and c? Find h:
Area of Triangle = ½ b*h
h
c
h = c (sin A)
sin A =
Area = ½ bc(sin A)
Theorem 9-1: Area of a Triangle Given SAS
Area of ΔABC = ½ bc(sin A)
Find area of this triangle to the nearest hundredth
A = ½ 5*9*sin(34) = 12.58 in2
Find area of these triangles to nearest tenth:
4/11/12
p.5
Elizabeth Pawelka
A = ½ 7*7*sin(31) = 12.6 ft2
Geometric Probability
A = ½ (7*10*sin(44)) = 24.3 m2
4/11/12
p.6
A = ½ * 8*6*sin(61) = 20.99 =
21 in2
Extension: If area of a triangle = ½ b*h and area of a parallelogram = b*h, what is the area of a
parallelogram given SAS?
Area of a parallelogram = bc(sin A):
Find area of this parallelogram to the nearest hundredth
A = 10*8*sin(63) = 71.28 m2
(Show Heron’s formula – p. 353: Challenge)
Find area of these regular polygons to nearest tenth
Elizabeth Pawelka
Geometric Probability
4/11/12
p.7
A dodecagon with perimeter = 108
½(central angle) = ½(45) = 22.5
cos(22.5) = a/10
a = 10*cos(22.5)
sin(22.5) = ½ b/10
½ b = 10sin(22.5)
b = 20sin(22.5)
p = 8*20sin(22.5)
A = ½(16.8)108 = 906.9 cm
A = ½ (10*cos(22.5)) * (8*20sin(22.5)) = 282.8 m
Closure (5 mins)


Today you learned to use trigonometry to find area of polygons.
Tomorrow we’ll review for the Chapter Test on Friday.
Homework (H)
 p. 500, # 1 – 18, 20, 21, 23, 25, 27
Homework (R)
 p. 500, # 1 – 18, 20, 21, 25
```
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