Module 6 Problems

  1. Find the supplement and the complement of a 53∘ angle.
  2. Find the supplement and the complement of a 16∘ angle.
  3. Find the supplement and the complement of a 29∘ angle.
  4. Find the supplement and the complement of a 72∘ angle.
  5. Find the supplement of a 135∘ angle.
  6. Find the complement of a 38∘ angle.
  7. Find the complement of a 27.5∘ angle.
  8. Find the supplement of a 109.5∘ angle.
  9. Two angles are supplementary. The larger angle is 56∘ more than the smaller angle. Find the measures of both angles.
  10. Two angles are supplementary. The smaller angle is 36∘ less than the larger angle. Find the measures of both angles.
  11. Two angles are complementary. The smaller angle is 34∘ less than the larger angle. Find the measures of both angles.
  12. Two angles are complementary. The larger angle is 52∘ more than the smaller angle. Find the measures of both angles.
  13. The measures of two angles of a triangle are 26∘ and 98∘. Find the measure of the third angle.
  14. The measures of two angles of a triangle are 61∘ and 84∘. Find the measure of the third angle.
  15. The measures of two angles of a triangle are 105∘ and 31∘. Find the measure of the third angle.
  16. The measures of two angles of a triangle are 47∘ and 72∘. Find the measure of the third angle.
  17. One angle of a right triangle measures 33∘. What is the measure of the other angle?
  18. One angle of a right triangle measures 51∘. What is the measure of the other angle?
  19. One angle of a right triangle measures 22.5∘. What is the measure of the other angle?
  20. One angle of a right triangle measures 36.5∘. What is the measure of the other angle?
  21. The two smaller angles of a right triangle have equal measures. Find the measures of all three angles.
  22. The measure of the smallest angle of a right triangle is 20∘ less than the measure of the other small angle. Find the measures of all three angles.
  23. Would you measure the amount of sand in a sandbag using linear, square or cubic measure?
  24. Would you measure the height of a tree using linear, square or cubic measure?
  25. Would you measure the size of a patio using linear, square or cubic measure?
  26. Would you measure the length of a highway using linear, square or cubic measure?
  27. The length of a rectangle is 42 meters and the width is 28 meters.  Find the perimeter and area.
  28. The length of a rectangle is 36 feet and the width is 19 feet. Find the perimeter and area.
  29. A sidewalk in front of Kathy’s house is in the shape of a rectangle 4 feet wide by 45 feet long.  Find the perimeter and are of the sidewalk.
  30. A rectangular room is 16 feet wide by 12 feet long.  Find the perimeter and area of the room.
  31. Find the length of a rectangle with perimeter of 220 centimeters and width of 85 centimeters.
  32. Find the width of a rectangle with perimeter 39 and length 11.
  33. The area of a rectangle is 2356 square meters. The length is 38 meters. What is the width?
  34. The width of a rectangle is 45 centimeters. The area is 2700 square centimeters. What is the length?
  35. The length of a rectangle is 12 centimeters more than the width. The perimeter is 74 centimeters. Find the length and the width.
  36. The width of a rectangle is 3 more than twice the length. The perimeter is 96 inches. Find the length and the width.
  37. Find the area of a triangle with base 18 inches and height 15 inches.
  38. Find the area of a triangle with base 33 centimeters and height 21 centimeters.
  39. A triangular road sign has base 30 inches and height 40 inches. What is its area?
  40. If a triangular courtyard has sides 9 feet and 12 feet and the perimeter is 32 feet, how long is the third side?
  41. A tile in the shape of an isosceles triangle has a base of 6 inches. If the perimeter is 20 inches, find the length of each of the other sides.
  42. Find the length of each side of an equilateral triangle with perimeter of 81 yards.
  43. The height of a trapezoid is 8 feet and the bases are 11 and 14 feet. What is the area?
  44. The height of a trapezoid is 5 yards and the bases are 7 and 10 yards. What is the area?
  45. Find the area of the trapezoid with height 25 meters and bases 32.5 and 21.5 meters.
  46. A flag is shaped like a trapezoid with height 62 centimeters and the bases are 91.5 and 78.1 centimeters. What is the area of the flag?
  47. Jose just removed the children’s playset from his back yard to make room for a rectangular garden. He wants to put a fence around the garden to keep out the dog. He has a 50 foot roll of fence in his garage that he plans to use. To fit in the backyard, the width of the garden must be 10 feet. How long can he make the other side if he wants to use the entire roll of fence?
  48. Lupita wants to fence in her tomato garden. The garden is rectangular and the length is twice the width. It will take 48 feet of fencing to enclose the garden. Find the length and width of her garden.
  49. Christa wants to put a fence around her triangular flowerbed. The sides of the flowerbed are 6 feet, 8 feet, and 10 feet. The fence costs $10 per foot. How much will it cost for Christa to fence in her flowerbed?
  50. A circular mosaic has radius 3 meters. Find the ⓐ circumference ⓑ area of the mosaic.  Round your answers to the nearest hundredth.
  51. A circular fountain has radius 8 feet. Find the ⓐ circumference ⓑ area of the fountain. Round your answers to the nearest hundredth.
  52. Find the diameter of a circle with circumference 150.72 inches.
  53. Find the radius of a circle with circumference 345.4 centimeters.
  54. Find the area of the shaded region.
  55. Find the area of the shaded region.  A geometric shape is shown. It is a U-shape. The base is labeled 5, the height 6. The horizontal and vertical lines at the top are labeled 2.  A geometric shape is shown, formed by two rectangles. The top is labeled 8. The width of the top rectangle is labeled 3. The right side of the figure is labeled 5. The width of the bottom rectangle is labeled 3.
  56. Find the area of the shaded region.  A geometric shape is shown. It is formed by two triangles. The shared base of the two triangles is labeled 20. The height of each triangle is labeled 15.
  57. Find the area of the shaded region.  A geometric shape is shown. It is a trapezoid with a triangle attached to the top on the right side. The height of the trapezoid is labeled 8, the bottom base is labeled 12, and the top is labeled 9. The height of the triangle is labeled 8.
  58. Find the area of the shaded region.A geometric shape is shown. It is a rectangle with a semi-circle attached to the top. The base of the rectangle, also the diameter of the semi-circle, is labeled 10. The height of the rectangle is labeled 16.
  59. Find the volume and surface area of a rectangular solid with length 14 centimeters, width 4.5 centimeters, and height 10 centimeters.
  60. Find the volume and surface area of a cube with sides that are 3 feet long.
  61. Find the volume and surface area of a cube of tofu with sides 2.5 inches.
  62. Find the volume and surface area of a rectangular carton with length 32 inches, width 18 inches, and height 10 inches
  63. Find the volume and surface area of a sphere with radius 4 yards.
  64. Find the volume and surface area of a sphere with radius 12 meters.
  65. Find the volume and surface area of a baseball with radius 1.45 inches.
  66. Find the volume and surface area of a soccer ball with radius 22 centimeters.
  67. Find the volume and surface area of a cylinder with radius 2 yards and height 6 yards.
  68. Find the volume and surface area of a cylinder with diameter 18 inches and height 40 inches.
  69. Find the volume and surface area of a juice can with diameter 8 centimeters and height 15 centimeters.
  70. Find the volume and surface area of a cylindrical pylon with diameter 0.8 feet and height 2.5 feet.
  71. Find the volume of a cone with height 5 meters and radius 1 meter.
  72. Find the volume of a cone with height 24 feet and radius 8 feet.
  73. Find the volume of a cone-shaped water cup with diameter 2.6 inches and height 2.6 inches.
  74. Find the volume of a cone-shaped pile of gravel with diameter 6 yards and height 5 yards.
  75. A rectangular moving van has length 16 feet, width 8 feet, and height 8 feet. How much can it hold?
  76. A rectangular gift box has length 26 inches, width 16 inches, and height 4 inches. How much can it hold?
  77. The base of a statue is a cube with sides 2.8 meters long. Find its volume and surface area.
  78. A box of tissues is a cube with sides 4.5 inches long. Find its volume and surface area.
  79. An exercise ball has a radius of 15 inches. Find its volume and surface area.
  80. A golf ball has a radius of 4.5 centimeters. Find its volume and surface area.
  81. A can of coffee has a radius of 5 cm and a height of 13 cm. Find its volume and surface area.
  82. A cylindrical column has a diameter of 8 feet and a height of 28 feet. Find its volume and surface area.
  83. What is the volume of a cone-shaped tee-pee tent that is 10 feet tall and 10 feet across at the base?
  84. What is the volume of a cone-shaped silo that is 50 feet tall and 70 feet across at the base?
  85. A regular ice cream cone is 4 inches tall and has a diameter of 2.5 inches. A waffle cone is 7 inches tall and has a diameter of 3.25 inches. To the nearest hundredth, ⓐ find the volume of the regular ice cream cone. ⓑ find the volume of the waffle cone. ⓒ how much more ice cream fits in the waffle cone compared to the regular cone?