Name:____________________________________________________ Hour__________

Final Exam Geometry Review Packet Semester II

1. _______ What is the length of the hypotenuse of a right triangle with leg lengths of 12 and 6?

A. 3√2 B. √144 C. 6√3 D. 6√5

2. _______ Find the unknown side length of the right triangle below. Write your answer in simplest radical form.

3. _______ An isosceles right triangle has leg lengths of 4 cm. Find the length of the hypotenuse. Round your answer to one decimal place.

4. _______ The length of one leg of a right triangle is 10 cm and the length of the hypotenuse is 20 cm. Find the length of the other leg. Write your answer in simplest radical form.

5. _______ Which of the following is not a Pythagorean triple or a multiple of a Pythagorean triple?

A. 10, 24, 26 B. 21, 72, 75 C. 8, 10, 12 D. 5, 12, 13

6. _______ What type of triangle has side lengths 25, 60, and 65?

A. Acute B. Right C. Obtuse D. Not a triangle.

7. _______Which side lengths do not form a right triangle?

A. 3, 6, 9 B. 4, 6, 9 C. 4, 5, 6 D. 3, 4, 5

8. _______Find the length of the hypotenuse. Write answer in simplest radical form.

9. _______Find the lengths of the legs.

A. 4 cm B. 4√2 cm C. 2√2 cm D. 8√2 cm

8

10. _______Find the values of x and y. Write your answers in simplest radical form.

Use the diagram for Exercises 11-13

11. _______ _______ Find the tan A and tan B. Round to 4 decimal places.

12. _______ _______ Find the sin A and sin B. Round to 4 decimal places.

13. _______ _______ Find the cos A and cos B. Round to 4 decimal places.

14. _______

15. _______

16. _______

17. _______

18. _______

19. a._______

b. _______

20. _______

21. _______

22. _______ Find the lengths of the sides of the right triangle. Round answers to nearest tenth.

23. _______ Find the lengths of the sides of the right triangle. Round answers to nearest tenth.

24. _______ The measures of three of the interior angels of a quadrilateral are 109∘, 114

∘ and 75

∘.

What is the measure of the fourth interior angle?A. 52

∘B. 85

∘C. 62

∘D. 75

∘

25. _______ Find the measure of an interior and an exterior angle of a regular hexagon.

30. _______

31.

32. _______

33. _______

34.

35. _______

36. _______

37. Points Q (0, 0), R (2, 4), S (4, 4) and T (4, 2) form a quadrilateral. Determine whether QRST is a kite. Explain.

__________________________________________________

38. _______Find m∠ A in the kite shown.

A. 88∘

B. 58∘

C. 90∘

D. 60∘

39. _______ What is the most specific name for the quadrilateral ABCD?

A. Rhombus B. Kite C. Square D. Parallelogram

40. A quadrilateral has at least one pair of opposite angles congruent. What types of quadrilaterals meet this condition? ________________________________________

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

51. Two sides of a triangle have lengths 7 and 13. The third side has a length that is ______.a. greater than 6 and less than 13b. less than 20 and greater than 6

c. greater than 2d. less than 6

52.

53. How many medians does a triangle have?

54.

55.

56.

57. _______Name a chord in Θ C.

58. _______Name a diameter in Θ C.

59. _______Name a radius in Θ C.

60. _______Which term best describes B⃗D ?A. radius B. chord C. tangent D. secant

61. _______Which term best describes D?A. point of tangency B. center C. common tangent D. radius

62. _______ In the diagram, A is a point of tangency. Find the radius r.

63. _______ What is the value of x?

Use the diagram for Exercises 64-68 . AD is a diameter of Θ C.

64. _______

65. _______

66. _______

67. _______A. 100

∘B. 150

∘C. 140

∘D. 130

∘

68. _______

57-61

A. 80∘

B. 100∘

C. 90∘

D. 12Use the diagram for Exercises 69 – 72. AB ¿ AC .

69. _______

70. _______A. 230

∘B. 225

∘C. 245

∘D. 240

∘

71. _______ Suppose ED = 3x – 2 and FD = 5x – 8. Find the value of x.

72. _______ Suppose AB = 16 and ED = 4. What is AF?A. 2 B. 4 C. 6 D. 8

73. _______ Suppose CD = 6x – 3 and FD = x + 2. Find the value of x.

74. _______ Suppose = (3x – 5)∘

and m = (5x – 35)∘

. What is m ?A. 90

∘B. 80

∘C. 180

∘D. 100

∘

75. _______ Find ST and QT.

76. _______ Find the value of x.

77. _______What is the value of x? Round to the nearest tenth. A. 0.8 B. 4.6 C. 6.0 D. 6.8

78. _______ What is the value of x?79. _______ What is the value of y?

73 and 74

78 and 79

A. 20 B. 22 C. 24 D. 25

Use the diagram in Exercises 80 and 81.80. _______ Find m∠BAC .

81. _______What is m∠ ABC?

A. 56∘

B. 60∘

C. 68∘

D.72∘

82. _______In the diagram, what is the value of x?A. 102

∘B. 156

∘C. 106

∘D. 78

∘

83. _________________________Write the standard equation of the circle with center (2, 3) and radius 7.

84. ___________________The point (-3, 2) is on a circle whose center is (3, -3). Write the standard equation of the circle.

85. _______ A parallelogram has a base of 6 cm and a height of 4 cm. What is the area?A. 12 cm

2B. 24 cm

2

C. 36 cm2

D. 48 cm2

86. The length of the hypotenuse of a right triangle is 25cm and the length of a leg is 15 cm._______a. Find the area of the triangle.

_______b. Find the perimeter.

87. _______ A rectangle has an area of 243 m2

and its length is triple its width._______a. Find the length.

_______b. Find the perimeter.

88. _______ Find the area of the given trapezoid.

89. _______A rhombus has an area of 45 cm2

and the length of one diagonal is 9 cm. What is the length of the other diagonal?

A. 5 cm B. 15 cmC. 20 cm D. 10 cm

90. _______The lengths of the diagonals of a kite are 16 cm and 21 cm. What is the area?

A. 84 cm2

B. 168 cm2

C. 336 cm2

D. 672 cm2

91. The lengths of the bases of two similar right triangles are 6 inches and 12 inches. The smaller triangle has an area of 42 square inches.

_______a. Find the height of the smaller triangle.

_______b. Find the area of the larger triangle.

92. _______The areas of two similar trapezoids are 24 m2

and 18 m2

. What is the ratio of the perimeter of the larger trapezoid to the perimeter of the smaller trapezoid?

A. 4 : 3 B. 4 : √3C. 2 : √3 D. 2 : 3

93. The side length of a regular hexagon is 11 feet._______a. Find the apothem. Round to one decimal place.

_______b. Find the area. Round to one decimal place.

94. _______Find the circumference of a circle with diameter 11 inches. Round to two decimal places.

95. _______ Find the approximate radius of a circle with circumference 23 meters. A. 3.66 m B. 7.32 mC. 36.13 m D. 72.26 m

96. _______Find the length of arc RS.

97. _______ Find the area of the shaded region.

98. _______ Find the area of the shaded region.

99. _______Which of the following solids has 12 edges?A. Rectangular Prism B. Triangular PrismC. Triangular Cylinder D. Square Pyramid

100. _______Tell whether the solid is a polyhedron. If it is, name the polyhedron and find the number of faces, vertices and edges.

101. _______ A solid has 12 edges and 6 faces. How many vertices does it have?A. 6 B. 8 C. 10 D. 12

102. _______How many faces and edges does a hexagonal pyramid have?A. 6 faces, 6 edges B. 7 faces, 12 edgesC. 4 faces, 14 edges D. 6 faces, 8 edges

103. _______What is the shape of the cross section formed by the plane perpendicular to the base through the top vertex of the square pyramid?

104. _______ The ratio of volumes of tow spheres is 1 : 27. What is the ratio of their surface areas?A. 1 : 3 B. 1 : 81C. 1 : 9 D. 3 : 81

105. _______Two similar solids have a scale factor of 1 : 3. Find the volume of the smaller solid if the volume of the larger solid is 54 cubic centimeters.

106. _______ Two triangular prisms are similar. The surface area of one prism is 70 square inches. The surface area of the other prism is 105 square inches. Find the scale factor of the smaller prism to the larger prism.

107. _______ What is the surface area of a right rectangular prism with height 3 inches, length 6 inches and width 12 inches?

A. 252 in.2

B. 108 in.2

C. 180 in.2

D. 216 in.2

108. _______What is the surface area of a right cylinder with a radius of 3 cm and a height of 6 cm?A. 27π cm

2B. 81π cm

2

C. 72π cm2

D. 54π cm2

109. _______ What is the area of a lateral face of a regular square pyramid with lateral edges of length 17 inches and base edges of length 10 inches.

A. 81.24 in 2

B. 85 in 2

C. 162.48 in 2

D. 170 in 2

110. _______ What is the surface area of a regular square pyramid with base edge length of 12 inches and a height of 10 inches?

A. 144 in2

B. 360 in2

C. 423.89 in2

D. 283.94 in2

111. _______What is the surface area of the right cone?

A. 48π m2

B. 52π m2

C. 60π m2

D. 85π m2

112. _______ The diameter of a sphere is 9 inches. Find the surface area of the sphere. Round your answer to two decimal places.

113. _______ The surface area of a sphere is 9π square meters. What is the radius of the sphere?

A. 1.5 m B. 3 mC. 4 m D. 6 m

114. _______What is the volume of a rectangular prism with height 3 inches, length 5 inches and width 9 inches?

A. 135 in 3

B. 108 in 3

C. 180 in 3

D. 216 in 3

115. _______Find the volume of the pyramid.

116. _______ What is the volume of a regular square pyramid with base edges of length 48 in.and a height of 10 in.?

A. 5760 in. 3

B. 23,040 in. 3

C. 7680in. 3

D. 2560 in. 3

117. _______A cone-shaped bottle has a radius of 18 centimeters at its base. If the bottle holds 6400 cubic centimeters when completely filled, what is its height?

A. 18.9 cm B. 19.8 cmC. 6.6 cm D. 6.3 cm

118. A sphere has a volume of 1316 cubic meters. Round your answers to two decimal places. ________a. Find the radius.

________b. Find the surface area.

119. _______ Which of the following is the net for a cube?

120. ________Which of the following is a net for a right cylinder.

121. A drawer contains 9 red socks, 2 white socks, and 7 blue socks. Without looking, you draw out a sock and then draw out a second sock without returning the first sock. What is the probability that the first sock and the second sock are both blue?

122. Of 100 students, 37 are taking Geometry, 52 are taking Spanish, and 11 are taking both Geometry and Spanish. If a student is picked at random, what is the probability that the student is taking Geometry or Spanish?

123. Each section of the spinner shown has the same area. The spinner was spun 30 times. The table shows the results. For which color is the experimental probability of stopping on the color the same as the theoretical probability?

124. A bag contains 9 tiles, one for each letter in the word HAPPINESS. You choose a tile at random. What is the probability that choose a tile with the letter S? What is the probability that you choose a tile with the letter other than P?

125. You throw a dart at the board shown. Your dart is equally likely to hit any point inside the square board. Are you most likely to get 5 points, 10 points, or 20 points?

126. You randomly select 2 cards from a standard deck of 52 playing cards. What is the probability that both cards are jacks when a.) you replace the first card before selecting the second and b.) you do not replace the first card?

127. Find the probability of randomly selecting the given marbles from a bag of 5 red, 8 green, and 3 blue marbles when a.) you replace the first marble before drawing the second, and b.) you do not replace the first marble.

i. Red, then green ii. Blue, then red iii. Green, then green

128. A survey asks residents of the east and west sides of a city whether they support the construction of a bridge. The results, given as joint relative frequencies, are shown in the two-way table.

a.)What is the probability that a randomly selected resident from the east side will support the project?

b.) What is the probability that a randomly selected resident who does not support the project is from the west side?

129. After a conference, 220 men and 270 women respond to a survey. Of those, 200 men and 230 women say the conference was impactful. Organize the results in a two-way table. Then find and interpret the marginal frequencies.

130. Make a two-way table that shows the joint and marginal relative frequencies.

131. Let A and B be events such that P(A) = ½ and P(A and B) = 1/3. Find P(A or B).

132. Let A and B be events such that P(A) = 0.32 and P(B) = 0.48, and P(A and B) = 0.12. Find P(A or B).

133. Out of 100 employees at a company, 92 employees either work part time or work 5 days each week. There are 14 employees who work part time and 80 employees who work 5 days each week. What is the probability that a randomly selected employee works both part time and 5 days each week?