1. Areas of Regular Polygons
May 9, 2003
Areas of Regular Polygons
GEOMETRY LESSON 7-5
Pages Exercises
1. m 1 = 120; m 2 = 60; m 3 = 30
2. m 4 = 90; m 5 = 45; m 6 = 45
3. m 7 = 60; m 8 = 30; m 9 = 60
cm2
ft2
6. 12,080 in.2
in.2 m2
cm2
ft2
in.2 m2
cm2
in.2
ft2 m2 m2
in.2
19. a. 72
b. 54
20. a. 45
b. 67.5
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2. Areas of Regular Polygons
May 9, 2003
Areas of Regular Polygons
GEOMETRY LESSON 7-5
21. a. 40
b. 70
22. a. 30
b. 75
ft2
24. a. 9.1 in.
b. 6 in.
c. 3.7 in.
24. (continued)
d. Answers may vary. Sample: About 4 in.; the length of a side of a pentagon should be between 3.7 in. and 6 in.
25. m 1 = 36; m 2 = 18; m 3 = 72
26. The apothem is one leg of a rt. and the radius is the hypotenuse.
cm2
in.2 m2
ft2
cm2
32. a–c.
regular octagon
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3. Areas of Regular Polygons
May 9, 2003
Areas of Regular Polygons
GEOMETRY LESSON 7-5
32. (continued)
d. Construct a 60° angle with vertex at circle’s center. m2
34. Check students’ work.
cm2
cm2, cm2
m2, m2 2 1 3
41. (continued)
b. apothem = ;
A = ap = (3s)
A = s2 3
s 3 6
ft2
in.2, 27.7 in.2
m2, 70.1 m2
41. a. b = s; h = s
A = bh
A = s • s
A = s
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4. Areas of Regular Polygons
May 9, 2003
Areas of Regular Polygons
GEOMETRY LESSON 7-5
42. The apothem is to a side of the pentagon. Two right are formed with the radii of the pentagon. So the are by HL. Therefore, the formed by the apothem and radii are by CPCTC, and the apothem bisects the vertex .
43. For regular n-gon ABCDE . . ., let P be the intersection of the bisectors of ABC and BCD. BC DC, BCP DCP, and CP CP, so BCP DCP, and CBP CDP by CPCTC. Since BCP is half the size of ABC and ABC CDE, CDP is half the size of CDE. By a similar argument, P is on the bisector of each around the polygon. s
43. (continued)
The smaller angles formed by the bisectors are all . By the Conv. of the Isosc. Thm., each of APB, BPC, CPD, and so on are isosceles with AP = BP = CP = DP and so on. Thus, P is equidistant from the polygon’s verticies, so P is the center of the polygon and the bisectors are radii.
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5. Areas of Regular Polygons
May 9, 2003
Areas of Regular Polygons
GEOMETRY LESSON 7-5 s 1 2
44. a. (2.8, 2.8)
b. 5.6 units2
c. 45 units2
45. a cm2 b.
46. B
47. F
48. B
5 3 3 4
49. [2] a. Divide the decagon into Consider one with hyp. of 35.6 and leg 11. The apothem can be found using the Pyth. Thm., so (35.6)2 – 112 = and leg in.
b. A (33.9)(220) = 3729 in.2
[1] incorrect calculation and correct explanation OR correct calculation and no explanation
50. [4] a. Area of BCG = bh = (8 3)(12) =
b. Area of ABCDEF = 6 • =
c. Find the area of one and mult. by 6 or use the formula for the area of a reg. polygon.
[3] appropriate methods, but with one computational error
[2] incorrect formulas OR no explanation
[1] incorrect calculations, correct explanation
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6. Areas of Regular Polygons
May 9, 2003
Areas of Regular Polygons
GEOMETRY LESSON 7-5 m2
in.
53. 8 m
DAB and CBA
ACG and BDF
DFA and CGB
57. a. 7.1 mi2
b. about 8 mi
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