FHC Geometry
Name: ________________________ Hour: ___
Second Semester Exam Review
Chapter 7
Are the polygons similar? If they are, write a similarity statement, and give the similarity ratio. If they are not, explain.
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The polygons are similar. Find the values of the variables.
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Explain why the triangles are similar. Write a similarity statement for each pair.
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Find the values of the variables.
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|13. |14. |15. |
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|16. |17. |18. |
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|19. Natasha places a mirror on the ground 24 ft from the base on an oak tree. |20. On page 370 of your Geometry text, there is a photo of a sandwich shop. |
|She walks backward until she can see the top of the tree in the middle of a |The sandwich shop is 40 ft tall. The sandwich shop is an enlargement of an |
|mirror. At that point, Natasha’s eyes are 5.5 ft above the ground, and her |actual milk bottle. The scale used in construction was 5 ft = 2 cm. Find the|
|feet are 4 ft from the image in the mirror. Find the height of the oak tree. |height of the actual milk bottle. |
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Chapter Ten
|48. Find the length of the missing leg of a right |49. Find the length of the hypotenuse of a right |50. Find the area of the shaded region. |
|triangle with one leg 6 cm and hypotenuse 13 cm. |triangle with legs 8 m and 7 m. Leave your answer |[pic] |
|Leave your answer in simplest radical form. |in simplest radical form. | |
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|51. Find the area of the shaded region. |52. Find the area of the parallelogram. |53. Find the area of the parallelogram. |
|[pic] |[pic] |[pic] |
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|54. Find the area of the trapezoid. Leave your |55. Find the area of the trapezoid. Leave your |56. Find the area of the trapezoid. Leave your |
|answers in simplest radical form. |answers in simplest radical form. |answers in simplest radical form. |
|[pic] |[pic] |[pic] |
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|57. Find the measure of each numbered angle in the regular polygon with radii |58. Find the measure of each numbered angle in the regular polygon with radii |
|and apothem as shown. |and apothem as shown. |
|[pic] |[pic] |
For each pair of similar figures, find the ratio of the perimeters and the ratio of their areas.
|59. |60. |61. |
|[pic] |[pic] |[pic] |
Find the area of each triangle. Round your answers to the nearest tenth.
|62. |63. |64. |
|[pic] |[pic] |[pic] |
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Find the area of each polygon. Round your answers to the nearest tenth.
|65. an equilateral triangle with apothem 5.8 cm |66. a square with radius 17 ft |67. a regular octagon with radius 20 in. |
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|68. Find the measure of each are in [pic] |69. Find the length of the arc. Leave your |70. Find the length of the arc. |
| |answer in terms of [pic] |Leave your answer in terms of [pic] |
|a. [pic] | | |
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|71. If a dart hits the board at the right, find | |72. If a dart hits the board at the right, find |
|the probability that it will land in region X. | |the probability that it will land in region Y. |
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|73. Find the circumference and area of a circle with radius 5 cm. Leave your answers in terms of [pic] |
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Chapter 11
|74. Find the lateral area and the surface area of the prism. |75. Find the lateral area and the surface area of the prism. |
|[pic] |[pic] |
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|Lateral Area: |Lateral Area: |
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|Surface Area: |Surface Area: |
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|76. Find the surface area of each cylinder in terms of [pic] |77. Find the surface area of each cylinder in terms of [pic] |
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|78. Find the surface area of a square pyramid with base length 16 cm and slant|79. Find the surface area of a square pyramid with base length 10 in. and |
|height 20 cm. |height 15 in. |
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|80. Find the lateral area of the cone to the nearest whole number. |81. Find the lateral area of the cone to the nearest whole number. |
|[pic] |[pic] |
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|82. Find the value of the variable in each figure. |83. Find the value of the variable in each figure. |84. Find the value of the variable in each figure. |
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|85. Find the volume of the pyramid. |86. Find the volume of the pyramid. |
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|87. Find the surface area of each sphere. Round your answers to the nearest |88. Find the surface area of each sphere. Round your answers to the nearest |
|tenth. |tenth. |
|[pic] |[pic] |
|89. Find the volume of each sphere. Round your answers to the nearest tenth. |90. Find the volume of each sphere. Round your answers to the nearest tenth. |
|[pic] |[pic] |
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|91. The figures in each pair are similar. Use the given information to find |92. The figures in each pair are similar. Use the given information to find |
|the similarity ratio of the smaller figure to the larger figure. |the similarity ratio of the smaller figure to the larger figure. |
|[pic] |[pic] |
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Chapter 12
In each diagram, a polygon circumscribes a circle. Find the perimeter of each polygon.
|93. |94. |
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Find the radius.
|95. |96. |97. |
|[pic] |[pic] |[pic] |
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Find the value of x to the nearest tenth.
|98. |99. |100. |
|[pic] |[pic] |[pic] |
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Write an equation for each circle with the given center that passes through the given point.
|101. center [pic]; point[pic] |102. center [pic]; point[pic] |103. center [pic]; point[pic] |
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Find the value of each variable.
|104. |105. |106. |
|[pic] |[pic] |[pic] |
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|107. |108. |109. |
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|110. |111. |112. |
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