Chapter 10 Practice Test
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1 Chapter 10 Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the area. The figure is not drawn to scale. 7.6 cm 3.7 cm a. b. c. d in. 40 in. 33 in. a in. 2 b. 69 in. 2 c. 138 in. 2 d in cm 5.4 cm a cm 2 b. 5.4 cm 2 c cm 2 d. 7.4 cm yd 10 yd a. 30 yd 2 b. 6.5 yd 2 c. 13 yd 2 d. 15 yd 2 5.
2 9 cm 8 cm 13 cm 9 cm 11 cm a cm 2 b. 127 cm 2 c. 172 cm 2 d. 50 cm 2 6. a. 188 in. 2 b. 278 in. 2 c. 322 in. 2 d. none of these in in in in. a in. 2 b in. 2 c in. 2 d in in. 7 in. 8 in. 12 in. Not drawn to scale a in. 2 b. 80 in. 2 c. 75 in. 2 d. 70 in The area of a parallelogram is 420 cm 2 and the height is 35 cm. Find the corresponding base. a. 385 cm b. 455 cm c. 14,700 cm 2 d. 12 cm Find the area of the trapezoid. Leave your answer in simplest radical form.
3 10. 8 ft 10 ft 60 Not drawn to scale a. 40 ft 2 b. 16 ft 2 c. 24 ft 2 d. 32 ft Find the area of the rhombus. 8 m 8 m 8 m 8 m a. 12 m 2 b m 2 c. 128 m 2 d. 32 m Find the area of the rhombus. Leave your answer in simplest radical form Not drawn to scale a. 50 b c d Given the regular hexagon, find the measure of each numbered angle.
4 3 1 2 a. c. b. d. 14. Find the area of a regular hexagon with an apothem 10.4 yards long and a side 12 yards long. Round your answer to the nearest tenth. a yd 2 b yd 2 c yd 2 d yd Find the area of a regular hexagon with side length of 8 m. Round your answer to the nearest tenth. a m 2 b m 2 c m 2 d. 288 m Find the area of an equilateral triangle with side 12. a. 36 b. 72 c. 36 d Find the area of the regular polygon. Round your answer to the nearest tenth in. 10 in. a in. 2 b in. 2 c in. 2 d in Find the area of an equilateral triangle with radius 8 m. Leave your answer in simplest radical form. a. 96 m 2 b. 144 m 2 c. 18 m 2 d. 12 m 2 The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to the second. The figures are not drawn to scale.
5 yd a. 40 yd and b. and c. and d. and a. 5 : 6 and 25 : 36 c. 5 : 6 and 36 : 49 b. 6 : 7 and 36 : 49 d. 6 : 7 and 25 : The widths of two similar rectangles are 16 cm and 14 cm. What is the ratio of the perimeters? Of the areas? a. 8 : 7 and 64 : 49 c. 9 : 8 and 81 : 64 b. 9 : 8 and 64 : 49 d. 8 : 7 and 81 : 64 The figures are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number. 22. The area of the larger triangle is 1589 ft. 40 ft 35 ft Not drawn to scale a ft b ft c ft d ft 23. The area of the smaller trapezoid is 558 m.
6 24 m 57 m Not drawn to scale a m b m c. 576 m d. 14 m 24. It costs a family $324 to buy a 10-ft-by-12-ft rug. At this rate, what will it cost them to buy a 15-ft-by-18-ft rug? a. $729 b. $270 c. $ d. $ Grade 7 students were surveyed to determine how many hours a day they spent on various activities. The results are shown in the circle graph below. Find the measure of each central angle in the circle graph. a. Sleeping b. Eating a ; 28.8 b. 108 ; 28.8 c ; 288 d ; Name the minor arc and find its measure. A D C ) 115 B a. arc ADB; 30 b. arc AB; 115 c. arc ADB; 245 d. arc AB; Name the major arc and find its measure.
7 A D C )50 B a. arc ADB; 50 b. arc AB; 50 c. arc ADB; 310 d. arc AB; Identify a semicircle that contains C. C A 0 B a. semicircle ABC c. semicircle CB b. semicircle AC d. semicircle ACB Find the circumference. Leave your answer in terms of cm a. cm b. cm c. cm d. cm in. a. in. b. in. c. in. d. in.
8 31. Find the length of arc XPY. Leave your answer in terms of. X 8 m Y P a. 24 m b. 12 m c. 4 m d. 720 m Find the area of the circle. Leave your answer in terms of m a m 2 b. 1.8 m 2 c m 2 d m m a m 2 b m 2 c m 2 d m Find the area of the figure to the nearest tenth a in. 2 b. 8.2 in. 2 c in. 2 d in Find the exact area of the shaded region.
9 a. c. b. d. none of these Short Answer 36. The regular polygon has radius 9 m. Find each angle measure to the nearest tenth of a degree, each linear measure to the nearest tenth of a meter, and the square measure to the nearest square meter. G H F E O A X B D C a. b. c. OX d. AB e. the perimeter f. the area Essay 37. a. Find the area of a regular hexagon with sides 2 cm long. Leave your answer in simplest radical form. b. Use your answer from part (a) to find the area of a regular hexagon of side length 8. Other 38. Write an explanation that justifies the statement: The area of a regular polygon is half the product of the apothem and the perimeter.
10 Chapter 10 Practice Test Answer Section MULTIPLE CHOICE 1. ANS: A STA: CA GEOM 8.0 CA GEOM 10.0 TOP: 10-1 Example 1 2. ANS: A STA: CA GEOM 8.0 CA GEOM 10.0 TOP: 10-1 Example 1 3. ANS: B STA: CA GEOM 8.0 CA GEOM 10.0 TOP: 10-1 Example 3 4. ANS: D STA: CA GEOM 8.0 CA GEOM 10.0 TOP: 10-1 Example 3 5. ANS: A STA: CA GEOM 8.0 CA GEOM 10.0 TOP: 10-1 Example 3 6. ANS: B STA: CA GEOM 8.0 CA GEOM 10.0 TOP: 10-1 Example 3 7. ANS: C STA: CA GEOM 8.0 CA GEOM 10.0 TOP: 10-2 Example 1 8. ANS: D STA: CA GEOM 8.0 CA GEOM 10.0 TOP: 10-2 Example 1 9. ANS: D STA: CA GEOM 8.0 CA GEOM 10.0 TOP: 10-1 Example ANS: D STA: CA GEOM 8.0 CA GEOM 10.0 TOP: 10-2 Example ANS: C STA: CA GEOM 8.0 CA GEOM 10.0 TOP: 10-2 Example ANS: D STA: CA GEOM 8.0 CA GEOM 10.0 TOP: 10-2 Example ANS: C STA: CA GEOM 8.0 CA GEOM 10.0 CA GEOM 20.0 TOP: 10-3 Example ANS: B STA: CA GEOM 8.0 CA GEOM 10.0 CA GEOM 20.0 TOP: 10-3 Example ANS: B STA: CA GEOM 8.0 CA GEOM 10.0 CA GEOM 20.0 TOP: 10-3 Example ANS: A STA: CA GEOM 8.0 CA GEOM 10.0 CA GEOM 20.0 TOP: 10-3 Example ANS: D STA: CA GEOM 8.0 CA GEOM 10.0 CA GEOM 20.0 TOP: 10-3 Example ANS: B STA: CA GEOM 8.0 CA GEOM 10.0 CA GEOM 20.0 TOP: 10-3 Example ANS: D STA: CA GEOM 11.0 TOP: 10-4 Example ANS: A STA: CA GEOM 11.0 TOP: 10-4 Example ANS: A STA: CA GEOM 11.0 TOP: 10-4 Example ANS: A STA: CA GEOM 11.0 TOP: 10-4 Example ANS: A STA: CA GEOM 11.0 TOP: 10-4 Example ANS: A STA: CA GEOM 11.0 TOP: 10-4 Example ANS: A STA: CA GEOM 7.0 CA GEOM 8.0 TOP: 10-6 Example ANS: B STA: CA GEOM 7.0 CA GEOM 8.0 TOP: 10-6 Example ANS: C STA: CA GEOM 7.0 CA GEOM 8.0 TOP: 10-6 Example ANS: D STA: CA GEOM 7.0 CA GEOM 8.0 TOP: 10-6 Example ANS: D STA: CA GEOM 7.0 CA GEOM 8.0 TOP: 10-6 Example ANS: B STA: CA GEOM 7.0 CA GEOM 8.0 TOP: 10-6 Example ANS: B STA: CA GEOM 7.0 CA GEOM 8.0 TOP: 10-6 Example ANS: C STA: CA GEOM 8.0 TOP: 10-7 Example ANS: A STA: CA GEOM 8.0 TOP: 10-7 Example ANS: A STA: CA GEOM 8.0 TOP: 10-7 Example ANS: B STA: CA GEOM 8.0 TOP: 10-7 Example 3
11 SHORT ANSWER 36. ANS: a b. 45 c. 8.3 m d. 6.9 m e m f. 229 m STA: CA GEOM 8.0 CA GEOM 19.0 ESSAY 37. ANS: [4] Answers may vary. Sample: a. The central angle of one of the triangles in the hexagon is. The altitude of the triangle is because it is a - - right triangle. 2 cm 1 cm The area of the hexagon is therefore. b. Because regular hexagons are similar, their areas will be proportional to the square of their similarity ratio.. cm 2. [3] correct methods but with a minor computational error [2] error in method [1] correct answer but with no work shown STA: CA GEOM 11.0 OTHER
12 38. ANS: Answers many vary. Sample: The apothem of a regular polygon is the height of one of n equal triangles into which the figure is divided. So, each triangle s area is, where s is the length of a side. The total area is. But sn is the perimeter, so the total area is. STA: CA GEOM 8.0 CA GEOM 10.0 CA GEOM 20.0 TOP: 10-3 Example 2
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