1. Trigonometry and Area Pages 500-503 Exercises 1. 173.8 cm2
GEOMETRY LESSON 9-5
Pages Exercises
cm2
in.2 m2
yd2
5. a. 72
b. 36
c. about 8.1 in.
d. about 11.8 in.
5. (continued)
e. about 58.8 in.
f. about 238 in.2
ft2
in.2
cm2
9. 8 ft2 m2 m2
ft2 m2
km2
mm2
ft2
yd2
18. a. 50 mm2
b. 116 mm2
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2. 28. (area of sq. A) = 4 • (area of sq. B)
Trigonometry and Area
GEOMETRY LESSON 9-5
19. Answers may vary.
Sample:
1. Find the apothem and the side to the apothem using a with hyp Then use the formula A = ap.
2. After finding the apothem and the side, the height of the equil is the apothem + 1. Then use the formula
A= bh
20. 1,459,000 ft2
21. $51.96
m; 20.8 m2
in.; 128 in.2
ft; 21.4 ft2
cm; cm2
m; m2
mi; 3 mi2
28. (area of sq. A) = 4 • (area of sq. B)
29. (area of pent. A) ≈ • (area of pent. B)
30. (area of hex. A) = (area of hex. B)
31. (area of oct. B) ≈ • (area of oct. A)
32. (area of dec. A) = • (area of dec. B)
ft2 1 2 1 2
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3. start to look like a circle of radius 1.
Trigonometry and Area
GEOMETRY LESSON 9-5
34. g. (continued)
start to look like a circle of radius 1.
35. Using steps similar to Ex. 34, A =
n cos sin ,
which also appr. as n increases.
36.
320 ft
34. (continued)
e. X tan(180/X)
f. X increases by 1 and Y1 approaches .
g. Answers may vary. Sample: 425; as X increases, Y1 approaches , so the first 4 viewable decimal places become fixed; the n-gons
180 n
34. a. Each central measures (360 ÷ n)
and m C =
that measure or (180 ÷ n).
b. tan C = = s
c. s = tan C, so p = n • 2(tan C) or 2n(tan C).
d. Since a = 1 and p = 2n(tan C), A =
ap = (1) (2n tan C) = n(tan C) s 1 2
tan
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4. c. The perimeter is (20)(5), or 100 yd. A = ap A = (10 tan 54°)(100)
Trigonometry and Area
GEOMETRY LESSON 9-5
38. B
39. G
40. B
41. [2]
42 sq. units, sq. units
41. (continued)
[1] Correct drawings OR correct solutions OR one correct drawing with solution
42. [4]
a. x = 54; tan 54° =
so a = 10 tan 54° yd
42. [4] (continued)
b. Use the formula
A= ap where A
represents the area, a represents the apothem, and p represents the perimeter.
c. The perimeter is (20)(5), or 100 yd.
A = ap
A = (10 tan 54°)(100)
688.2 yd2 a 10 1 2
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5. [3] appropriate methods, but with one computational error
Trigonometry and Area
GEOMETRY LESSON 9-5
376 45 25 4 63 8 a 2
, 0 , b
42. (continued)
[3] appropriate methods, but with one computational error
[2] correct answer but with no work shown
[1] correct answer to (a)
43. –2, –9
44. 6, 1
45. –6, –1
46. –2, –2 and 4, –2
cm2
in.2 m2
; a2 + 4b2
; a2 + b2
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