Intro to Section 95

1
Intro to Section 9-5
In this section, an attempt is made to show
students how trigonometry (and SohCahToa ?) can
be used to assist in solving geometric situations
other than right triangles. Here, well see how
to find the areas of uncooperative triangles and
shapes such as your basic regular polygons
(octagons, heptagons, allgons, etc.)
2
I. What is the formula for finding the area of a
Regular Polygon?
Where athe length of the apothem and pthe
perimeter
3
Find the area of a regular pentagon with 8-cm
sides to the nearest 1/10.
The triangle formed by an apothem and a radius is
not a special triangle What can we do?
8 cm
a
4
Find the area of a regular pentagon with 8-cm
sides to the nearest 1/10.
8 cm
Well use trig! Woo hoo!
a
5
Find the area of a regular pentagon with 8-cm
sides to the nearest 1/10.
8 cm
And heres how
a
6
Find the area of a regular pentagon with 8-cm
sides to the nearest 1/10.
Determine the measure of a central angle (in this
case 3605)
8 cm
72
a
7
Find the area of a regular pentagon with 8-cm
sides to the nearest 1/10.
Notice the apothem bisects the central angle,
creating a 36 angle inside the blue right
triangle
8 cm
72
36
a
8
Find the area of a regular pentagon with 8-cm
sides to the nearest 1/10.
Which leaves a 54 angle down at the vertex of
the shape. We can also put a 4 on the leg (the
apothem bisects a side)
8 cm
72
36
a
54
4
9
Find the area of a regular pentagon with 8-cm
sides to the nearest 1/10.
Its time to solve the problem!
8 cm
72
36
a
54
4
10
Find the area of a regular pentagon with 8-cm
sides to the nearest 1/10.
8 cm
72
36
a
54
4
11
Find the area of a regular pentagon with 8-cm
sides to the nearest 1/10.
8 cm
72
36
a
54
4
12
II. What is the formula for finding the area of
a triangle?
B
a
c
h
A
C
b
SO
13
Theorem 9-1 Area of a Triangle
given SAS The area of a triangle
is one half the product of the lengths of two
sides and the sine of the included angle.
B
a
c
A
C
b
14
Samples Find the area of ?ABC
to the nearest tenth.
B
412 ft
C
A
386 ft
15
Two sides of a triangular building plot are 120
ft and 85 ft long. They include an angle of 67
degrees. Find the area of the building plot to
the nearest square foot.
85
67
120
16
Try this oneFind the area of a regular octagon
to the nearest hundredth if a side12 in.
17
Find the area of a regular octagon to the nearest
hundredth if a side12 in.
One central ? is 3608 (45) which when bisected
creates a 22.5 and a 67.5? inside the
apothem/radius ?, and one side6
22.5
a
67.5
6
18
Find the area of a regular octagon to the nearest
hundredth if a side12 in.
22.5
a
67.5
6
19
Find the area of a regular octagon to the nearest
hundredth if a side12 in.
22.5
a
67.5
6