Name: ________________________ Class: ___________________ Date: __________
ID: A
Geometry Spring Final Review #1, 2014 Short Answer 1. Find the measure of each interior angle of a regular 45-gon.
2. Find the measure of each exterior angle of a regular decagon.
3. The door on a spacecraft is formed with 6 straight panels that overlap to form a regular hexagon. What is the measure of ÐYXZ?
4. The diagram shows the parallelogram-shaped component that attaches a car’s rearview mirror to the car. In parallelogram RSTU, UR = 25, RX = 16, and mÐSTU = 42.4o. Find ST, XT, and mÐRST.
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Name: ________________________
ID: A
5. MNOP is a parallelogram. Find MP.
6. An artist designs a rectangular quilt piece with different types of ribbon that go from the corner to the center of the quilt. The dimensions of the rectangle are AB = 10 inches and AC = 14 inches. Find BX .
7. TRSU is a rhombus. Find SU .
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Name: ________________________
ID: A
8. A pillow is the shape of a kite. Heath wants to create a design connecting opposite corners from point B to point D, and from point A to point C. Find the amount of cording needing. One package of cording contains 5 inches of cord. How many packages does Heath need?
9. In kite PQRS, mÐQPO = 50° and mÐQRO = 70°. Find mÐPSR.
10. Given isosceles trapezoid ABCD with AB @ CD, BY = 10.3, and AC = 17.2. Find YD.
11. Given that two points on line m are P(7, 11) and Q(12, 9), write a ratio expressing the slope of m.
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Name: ________________________
ID: A
12. The ratio of the side lengths of a quadrilateral is 6:2:3:7, and its perimeter is 126 meters. What is the length of the shortest side?
13. Solve the proportion
6 21 = . 7 10w
14. Coby designs a rectangular vegetable garden. What will be the length of the full-size vegetable garden?
15. Identify the pairs of congruent angles and proportional corresponding side lengths.
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Name: ________________________
ID: A
16. Determine whether the rectangles are similar. If so, write the similarity ratio and a similarity statement.
17. Maya is making a miniature dinner table for her little sister. She wants the table top to be similar to their real dinner table top. Find the width of the miniature table top to the nearest tenth of a centimeter.
18. A video game designer is modeling a tower that is 320 ft high and 260 ft wide. She creates a model so that the similarity ratio of the model to the tower is
1 500
. What is the height and the width of the model in inches?
19. Explain why the triangles are similar and write a similarity statement.
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Name: ________________________
ID: A
20. Verify that DPQR ~ DSQT .
21. Explain why DABC ~ DDBE and then find BC.
22. To find out how wide a river is, John and Sally mark an X at the spot directly across from a big rock on the other side of the river. Then they walk in a straight line along the river, perpendicular to the straight line between the X and the rock. After walking for 20 feet Jon stops while Sally continues along the straight line for another 10 feet. Then she makes a 90 degree turn and walks for 30 feet. When she stops and looks at the rock she sees that the straight line from her to the rock passes through John. What is the distance from X to the rock?
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Name: ________________________
ID: A
23. Find NP.
24. A tree is standing next to a 40-foot high building. The tree has an 18-foot shadow, while the building has a 16-foot shadow. How tall is the tree, rounded to the nearest foot?
25. A model airplane is built to a scale of 1 in.:12 ft. If the model plane is 11 inches long, find the length of the actual plane, rounded to the nearest foot.
26. A house is 32 feet wide and 60 feet long. If a sketch is made of the house using the scale 1 cm: 4 ft, what are the dimensions of the sketch?
27. The city of Bangor, Maine has a scale model of Paul Bunyan nearly 30 feet tall. The model’s scale is 1:5. On the scale model, Paul Bunyan’s belt buckle is 12 feet from the ground. In real life, how far from the ground is Paul Bunyan’s belt buckle? The diameter of Paul Bunyan’s actual head is 9 inches. What is the diameter of the Paul Bunyan’s scale model head in feet?
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Name: ________________________
ID: A
28. Write the trigonometric ratio for cos X as a fraction and as a decimal rounded to the nearest hundredth.
29. Use a special right triangle to write tan 60° as a fraction.
30. Use your calculator to find trigonometric ratios sin 79°, cos 47°, and tan 77°. Round to the nearest hundredth.
31. Find GH. Round to the nearest hundredth.
32. Jessie is building a ramp for loading motorcycles onto a trailer. The trailer is 2.8 feet off of the ground. To avoid making it too difficult to push a motorcycle up the ramp, Jessie decides to make the angle between the ramp and the ground 15°. To the nearest hundredth of a foot, find the length of the ramp.
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Name: ________________________
ID: A
33. Use your calculator to find the angle measures sin -1 (0.35), cos -1 (0.9), and tan -1 (49.5) to the nearest tenth of a degree.
34. Find sinÐA to the nearest hundredth.
35. Some mountains in the Alps are very steep and have a grade of 42.7%. To the nearest degree, what angle do these mountains make with a horizontal line?
36. Classify each angle in the diagram as an angle of elevation or an angle of depression.
37. The largest Egyptian pyramid is 146.2 m high. When Rowena stands far away from the pyramid, her line of sight to the top of the pyramid forms an angle of elevation of 20° with the ground. What is the horizontal distance between the center of the pyramid and Rowena? Round to the nearest meter.
38. An eagle 300 feet in the air spots its prey on the ground. The angle of depression to its prey is 15°. What is the horizontal distance between the eagle and its prey? Round to the nearest foot.
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Name: ________________________
ID: A
39. A pilot flying at an altitude of 1.8 km sights the runway directly in front of her. The angle of depression to the beginning of the runway is 31°. The angle of depression to the end of the runway is 23°. What is the length of the runway? Round to the nearest tenth of a kilometer.
40. Find the area of the parallelogram.
41. Find the area of a trapezoid, in which b 1 = 13 cm, b 2 = 16 cm, and h = 3 cm.
42. Find the area of the rhombus.
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Name: ________________________
ID: A
43. The vertices of square ABCD are the midpoints of the sides of a larger square. Find the perimeter and the area of square ABCD. Round to the nearest hundredth.
44. Find h in the parallelogram.
45. Find the area of –Q in terms of p .
46. A store sells circular rugs in three different sizes. The rugs come in diameters of 8 ft, 12 ft, and 16 ft. Find the areas of the three different sizes of rugs. Use 3.14 for p and round answers to the nearest tenth.
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Name: ________________________
ID: A
47. Find the area of a regular hexagon with side length 4 m. Round to the nearest tenth.
48. Two circles have the same center. The radius of the larger circle is 3 units longer than the radius of the smaller circle. Find the difference in the circumferences of the two circles. Round to the nearest hundredth.
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Name: ________________________
ID: A
49. Find the area of the composite figure.
50. Find the shaded area. Round to the nearest tenth.
51. Find the volume of a right rectangular prism with length 12 in., width 10 in., and height 6 in. Round to the nearest tenth, if necessary.
52. A fish tank is in the shape of a rectangular prism. The height of the tank is 18 in. The width of the tank is 17 in. The length of the tank is 38 in. Find the amount of water the tank can hold to the nearest gallon. (Hint: 1 gallon » 0.134 ft3.)
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Name: ________________________
ID: A
53. Find the volume of a cylinder with a base area of 25p in 2 and height equal to the radius. Give your answer both in terms of p and rounded to the nearest tenth.
54. Find the volume of the three-dimensional figure in terms of x.
55. Find the diameter of a sphere with volume 972p in3.
56. Find the volume of a sphere with diameter 30 ft. Give your answer in terms of p .
57. Find the surface area of a sphere with volume 288p m3. Give your answer in terms of p .
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ID: A
Geometry Spring Final Review #1, 2014 Answer Section SHORT ANSWER 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
172° 36° mÐYXZ = 60o ST = 25, mÐRST = 137.6°, XT = 16 MP = 30 BX = 7 inches SU = 7 about 20.2 in., 5 packages mÐPSR = 60° YD = 6.9
11. - 5 2
12. 14 meters 13. w =
49 20
14. 144 in. 15. ÐB @ ÐD, ÐC @ ÐE, ÐA @ ÐF , 16. The similarity ratio is
EF DF DE 3 = = = AC AB BC 4
3 and rectangle MNOP ~ rectangle RSTU. 5
17. 4.9 cm 18. height = 7.68 in.; width = 6.24 in. 19. ÐA @ ÐBDE and ÐC @ ÐBED by the Corresponding Angles Postulate. DABC ~ DDBE by AA Similarity. 20. ÐQ @ ÐQ by the Reflexive Property of Congruence. QS QT 3 = = QP QR 5 DPQR ~ DSQT by SAS Similarity. 21. AC € DE by the Converse of the Corresponding Angles Postulate. ÐA @ ÐBDE by the Corresponding Angles Postulate. DABC ~ DDBE by AA Similarity. Corresponding sides are proportional, so BC = 42. 22. 60 feet 23. NP = 1.25 24. 45 feet 25. 132 feet 26. 8 cm ´ 15 cm 27. 2.4 feet; 3.75 feet
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ID: A
28. cos X = 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39.
12 = 0.80 15
3 1 sin 79° = 0.98, cos 47° = 0.68, tan 77° = 4.33 GH = 22.46 in. 10.82 feet sin -1 (0.35) = 20.5º, cos -1 (0.9) = 25.8º, tan -1 (49.5) = 88.8º sinÐA = 0.45 23° Angles of elevation: Ð1, Ð3 Angles of depression: Ð2, Ð4 402 m 1,120 ft 1.2 km
40. 28 in 2 41. 43.5 cm2 42. (30x 2 + 50x + 20) cm 2 43. perimeter = 14.14 cm; area = 12.5 cm 2 44. 9.6 units 45. 100p cm 2 46. 50.2 ft2; 113.0 ft2; 201.0 ft2 47. 41.6 m2 48. 18.84 units 49. 378 ft2 50. 20.2 in 2 51. 720 in3 52. 50 gallons 53. 125p in 3 » 392.7 in 3 54. 55. 56. 57.
6x 3 + 3x 2 18 in. 4,500p ft3 144p m2
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