Name: ___________________________________________________ Period: ______ Date: ____________________

1

Geometry 2 Final Review

1 Find x in ABC.

2 Find x in STU.

3 Find y in XYZ.

4 Find x in HJK.

5 Find x in ABC.

6 Find cos A in ABC.

7 Find x to the nearest tenth.

8 Find the angle of elevation of the sun when a

pole 25 feet tall casts a shadow 42 feet long.

9 Find the geometric mean between 7 and 12.

2

10 Find x.

11 Find y.

12 Find x.

13 Find c.

14 Find the perimeter of a square if the length of its

diagonal is 12 inches. Round to the nearest tenth.

15 Find x to the nearest degree.

16 If a 20-foot ladder makes a 65° angle with the

ground, how many feet up a wall will it reach?

Round your answer to the nearest tenth.

17 Given A(3, −7), under which reflection is A′(3,

7)?

A reflection in the x-axis

B reflection in the y-axis

C reflection in the origin

D reflection in the line y = x

18 Find the magnitude of the rotational symmetry in

a regular pentagon.

19 Find the coordinates of X ′ with X(-6, 5) for a

dilation centered at the origin with a scale factor

of −3.

20 Given B(−4, −6), under which reflection is B′(4,

6)?

A reflected in the x-axis

B reflected in the y-axis

C reflected in the origin

D reflected in the line y = x

3

21 Name the image of EF under reflection in

FH→← .

A FG

B HG

C EH

D FE

22 Find the scale factor if D ′E′F ′ is the image of

DEF under a dilation with center C.

23 Find the reflection of the point A(6, −1) across

the line y = x.

24 Write the coordinates of the image of P(−2, 5)

reflected in the line y = x.

25 Find the image of WX with W(7, 1) and X(−4, 5)

under the translation (x, y) → (x − 4, y − 3).

26 Find the image of AB with A(−3, 1) and B(−1, 5)

under a rotation of 90° clockwise about the

origin.

27 Find the measure of the image of ST if ST = 4

under a dilation with a scale factor of 3

4.

28 If ST = 12 and S ′T ′ = 9, find the scale factor of

the dilation.

29 Given ABC with vertices A(1, 0), B(6, −7), and

C(0, −4). Find the coordinates of the vertices of

the triangle under the translation (x, y) → ( x, y

−4).

30 In C, mAB = 72. Find m∠BCD.

31 Find the length of PQ in R to the nearest

hundredth.

4

32 In O, AB = 12 centimeters, OE = 4 centimeters,

and OF = 4 centimeters. Find CF.

33 Find the radius of a circle if a 48-meter chord is 7

meters from the center.

34 Find m∠ABC.

35 Find x.

36 Find y.

37 Find z.

38 Find x.

39 Identify the graph of (x − 3)2 + (y + 2)2 = 4.

A

B

C

D

5

40 Find x.

41 The diameter of a circular swimming pool is 15

feet. Find the circumference to the nearest

hundredth.

42 In A, m∠BAD = 110. Find mDE.

43 Points X and Y lie on P so that PX = 5 meters

and m∠XPY = 90. Find the length of XY to the

nearest hundredth.

44 Chords XY and WV are equidistant from the

center of O. If XY = 2x + 30 and WV = 5x − 12,

find x.

45 Find the radius of O if DE = 12 inches and DE

bisects OF.

46 Find x.

47 EFGH is a quadrilateral inscribed in P with

m∠E = 72 and m∠F = 49. Find m∠G.

48 If AB is tangent to C at A, find BC.

6

49 PQ, QR, RS, and SP are tangent to X. Find the

perimeter of PQRS.

50 Find x.

51 Find y.

52 Find z.

53 Find the center of the circle whose equation is (x

+ 11)2 + (y − 7)2 = 121.

54 Find the equation of P.

55 Find YB if the diameter of A is 10 inches, the

diameter of B is 8 inches, and AX = 3 inches.

56 In K, m∠HKG = x + 10 and m∠IKJ = 3x − 22.

Find mFJ .

57 The diameter of C is 18 units long. Find the

length of an arc that has a measure of 100. Round

to the nearest hundredth.

7

58 In A, CG = 5x + 2 and GD = 7x − 12. Find x.

59 In O, PQ = 18 meters. Find the distance from

O to PQ.

60 Find x.

61 Find x.

62 Find x if BA→

is tangent to P at A.

63 Write the equation of a circle with a diameter

having endpoints at (−2, 6) and (8, 4).

64 Write the equation of a circle with a radius of 10

and a center at (−4, −9).

65 Find the area of parallelogram WXYZ. Round to

the nearest tenth.

66 Find the area of quadrilateral DEFG.

8

67 Find the area of a regular octagon with a

perimeter of 96 centimeters.

68 Find the area of an equilateral triangle with a side

length of 14 inches.

69 Find the probability that a point chosen at

random lies in the shaded sector.

70 Find the area of the shaded segments.

71 A rhombus has an area of 165 square units. If the

length of one of its diagonals is 15 units, find the

length of its other diagonal.

72 Find the area of a regular hexagon with side

length of 10 centimeters. Round to the nearest

tenth.

73 Find the area of a nonagon with a perimeter of

126 inches. Round to the nearest tenth.

74 Find the area of the shaded region. Round to the

nearest tenth.

75 A running track consists of two parallel lines that

are connected at each end by the curved

boundary of a semicircle. The parallel lines are

30 meters long and 7 meters apart. Find the area

of the running track.

76 Find the probability that a point chosen at

random lies in the shaded region.

Find the area of each parallelogram. Round to

the nearest tenth if necessary.

77

9

78 The area of parallelogram ABCD is 2250 square

meters. Find the lengths of the height and base.

Find the area of each polygon. Round to the

nearest tenth.

79 a square with a perimeter of 16 2 inches

80 a regular hexagon with apothem length of 4.3

centimeters

81 A children’s game is won by tossing a coin so

that it lands on the white part of this board. If one

coin is tossed, what is the probability of winning?

82 If the length of the height of a trapezoid is 4

meters, the length of one of its bases is 11 meters,

and its area is 62 square meters, then what is the

measure of the other base?

83 Find the surface area of a rectangular prism with

a length of 8 inches, a width of 5 inches, and a

height of 2 inches.

84 The lateral area of a regular pyramid is 300

square units. The perimeter of its base is 100

units. Find the slant height of the pyramid.

Refer to the figure.

85 Find the lateral area.

86 The radius of a cone is 17 inches long and the

slant height is 20 inches. Find the surface area to

the nearest tenth.

87 The diameter of a sphere is 42 centimeters. Find

the surface area to the nearest tenth.

10

88 Find the surface area of the prism.

89 The surface area of a right cylinder is 200π

square centimeters and the radius is 4

centimeters. Find the height of the cylinder.

Use a right cylinder with a radius of 3 inches

and a height of 17 inches. Round to the nearest

tenth.

90 Find the lateral area.

91 Find the surface area.

Refer to the figure.

92 Find the surface area.

Refer to the figure. Round to the nearest

tenth.

93 Find the lateral area.

94 Find the surface area to the nearest tenth.

95 Find the surface area of the solid.

96 Find the lateral area of a right cylinder with a

diameter of 8.6 yards and a height of 19.4 yards.

Round to the nearest tenth.

97 Find the lateral area of the triangular pyramid.

11

98 The surface area of a regular pyramid is 276

square centimeters, the slant height measures 8

centimeters, and the area of the base is 50 square

centimeters. Find the perimeter of the base.

99 Plane A intersects sphere R in X. Find the

radius of the sphere.

100 Find the surface area of this hemisphere to the

nearest tenth.

101 The volume of a cylinder is 62.8 cubic meters

and the radius is 2 meters. Find the height of the

cylinder. Round to the nearest meter.

102 Find the volume of the pyramid.

103 Find the volume of the oblique cone. Round to

the nearest tenth.

104 A sphere has a radius that is 12 centimeters long.

Find the volume of the sphere. Round to the

nearest tenth.

105 A sphere has a volume that is 36π cubic meters.

Find the radius of the sphere.

106 A cylinder whose height is 5 meters has a volume

of 320π cubic meters. Find the radius of the

cylinder.

107 A square pyramid has a height that is 8

centimeters long and a base with sides that are

each 9 centimeters long. Find the volume of the

pyramid.

108 The volume of a cone is 1080π cubic centimeters

and the radius is 18 centimeters. Find the height

of the cone.

12

109 Find the volume to the nearest tenth.

110 A sphere has a volume of 972π cubic inches.

Find the radius of the sphere.

111 The ratio of the radii of two similar cylinders is

3:5. The volume of the smaller cylinder is 54π

cubic centimeters. Find the volume of the larger

cylinder.

112 The ratio of the heights of two similar solids is

7:9. Find the ratio of their volumes.

113 A box has a length of 12 inches, a width of 9

inches, and a height of 4 inches. Find the volume

of the box.

114 Find the volume of the cylinder. Round to the

nearest tenth.

115 A regular hexagonal pyramid has a height that is

15 feet and a base 6 feet on each side. Find the

volume of the pyramid.

116 The volume of a pyramid is 120 cubic inches and

the area of the base is 50 square inches. Find the

height of the pyramid.

117 The surface area of a sphere is 804.2 square

inches. Find the volume of the sphere. Round to

the nearest cubic inch.

118 Find the volume of the solid. Round to the

nearest tenth.

119 The ratio of the heights of two similar prisms is

2:7. The surface area of the smaller prism is 50

square meters. Find the surface area of the larger

prism.

120 The ratio of the volumes of two similar solids is

8:27. Find the ratio of their surface areas.