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Geometry Word Problems Practice Questions Set 4

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Updated on Sep 26, 2011

Geometry Word Problems

The geometry problems in this set  involve lines, angles, triangles, rectangles, squares, and circles. You will learn how to find length, perimeter, area, circumference, and volume, and how you can apply geometry to everyday problems.

  1. Find the surface area of the monument to the nearest meter.
    1. 13,820 m2
    2. 13,451 m2
    3. 3,455 m2
    4. 13,543 m2
  2. An inground pool is filling with water. The shallow end is 3 ft deep and gradually slopes to the deepest end, which is 10 ft deep. The width of the pool is 15 ft and the length is 30 ft. What is the volume of the pool?
  3. Geometry

    1. 1,575 ft3
    2. 4,500 ft3
    3. 2,925 ft3
    4. 1,350 ft3

For questions 3 and 4, refer to the following illustration:

Geometry

  1. In a periscope, a pair of mirrors is mounted parallel to each other as shown. The path of light becomes a transversal. If 2 measures 50°, what is the measurement of 3?
    1. 50°
    2. 40°
    3. 130°
    4. 310°
  2. Given that 2 measures 50°, what is the measurement of 4?
    1. 50°
    2. 40°
    3. 130°
    4. 85°
  3. The angle measure of the base angles of an isosceles triangle are represented by x and the vertex angle is 3x + 20. Find the measure of a base angle.
    1. 116°
    2. 40°
    3. 32°
    4. 14°
  4. Using the information from question 440, find the measure of the vertex angle of the isosceles triangle.
    1. 32°
    2. 62°
    3. 58°
    4. 116°
  5. In parallelogram ABCD, A = 5x + 2 and C = 6x –4. Find the measure of A.
    1. 32°
    2. 84.7°
    3. 44°
  6. The longer base of a trapezoid is three times the shorter base. The nonparallel sides are congruent. The nonparallel side is 5 cm more that the shorter base. The perimeter of the trapezoid is 40 cm. What is the length of the longer base?
    1. 15 cm
    2. 5 cm
    3. 10 cm
    4. 21 cm
  7. The measure of the angles of a triangle are represented by 2x + 15, x + 20, and 3x + 25. Find the measure of the smallest angle within the triangle.
    1. 40°
    2. 85°
    3. 25°
    4. 55°
  8. Suppose ABCD is a rectangle. IF to the nearest tenth.
  9. Geometry

    1. 4.0
    2. 5.8
    3. 11.7
    4. 8.0
  10. The perimeter of the parallelogram is 32 cm. What is the length of the longer side?
  11. Geometry

    1. 9 cm
    2. 10 cm
    3. 6 cm
    4. 12 cm
  12. A door is 6 feet and 6 inches tall and 36 inches wide. What is the widest piece of sheetrock that can fit through the door? Round to the nearest inch.
    1. 114 in
    2. 86 in
    3. 85 in
    4. 69 in
  13. The width of a rectangle is 20 cm. The diagonal is 8 cm more than the length. Find the length of the rectangle.
    1. 20
    2. 23
    3. 22
    4. 21
  14. The measures of two complementary angles are in the ratio of 5:7. Find the measure of the smallest angle.
    1. 75°
    2. 37.5°
    3. 52.5°
    4. 105°
  15. In parallelogram ABCD, m A = 3x + 10 and mD = 2x + 30, find the mA.
    1. 70°
    2. 40°
    3. 86°
    4. 94°
  16. Using the diagram below and the fact that A + B + C + D = 320, find mE.
  17. Geometry

    1. 80°
    2. 40°
    3. 25°
    4. 75°
  18. The base of a triangle is 4 times as long as its height. If together they measure 95 cm, what is the area of the triangle?
    1. 1,444 cm2
    2. 100 cm2
    3. 722 cm2
    4. 95 cm2
  19. One method of finding the height of an object is to place a mirror on the ground and then position yourself so that the top of the object can be seen in the mirror. How high is a structure if a person who is 160 cm tall observes the top of a structure when the mirror is 100 m from the structure and the person is 8 m from the mirror?
  20. Geometry

    1. 50,000 cm
    2. 20,000 cm
    3. 2,000 cm
    4. 200 cm
  21. Suppose ABCD is a parallelogram; B = 120 and 2 = 40. Find m 4.
  22. Geometry

    1. 50°
    2. 40°
    3. 20°
    4. 30°
  23. The length and width of a rectangle together measure 130 yards. Their difference is 8 yards. What is the area of the rectangle?
    1. 4,209 yd2
    2. 130 yd2
    3. 3,233 yd2
    4. 4,270 yd2
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