GED Mathematical Reasoning Preparation Course: GED geometry and measurement

1. Frage 1 von 17

   A rectangular yard is 14 feet long and 9 feet wide. What is its perimeter?

   • A37 feet
   • B126 feet
   • C23 feet
   • D46 feet
   Antwort anzeigen

   Antwort: D. 46 feet

   Perimeter of a rectangle = 2l + 2w = 2(14) + 2(9) = 46 feet.

2. Frage 2 von 17

   A room is 12 feet by 15 feet. How much carpet covers the floor?

   • A54 square feet
   • B360 square feet
   • C180 square feet
   • D27 square feet
   Antwort anzeigen

   Antwort: C. 180 square feet

   Area of a rectangle = length × width = 12 × 15 = 180 square feet.

3. Frage 3 von 17

   A triangle has a base of 10 inches and a height of 7 inches. What is its area?

   • A35 square inches
   • B17 square inches
   • C70 square inches
   • D24.5 square inches
   Antwort anzeigen

   Antwort: A. 35 square inches

   Area of a triangle = 1/2 × base × height = 1/2 × 10 × 7 = 35 square inches.

4. Frage 4 von 17

   A circle has a radius of 5 inches. Using π ≈ 3.14, what is its area?

   • A78.5 square inches
   • B31.4 square inches
   • C314 square inches
   • D15.7 square inches
   Antwort anzeigen

   Antwort: A. 78.5 square inches

   Area = πr² = 3.14 × 5 × 5 = 78.5 square inches. 31.4 is the circumference, not the area.

5. Frage 5 von 17

   A round table has a diameter of 14 inches. Using π ≈ 3.14, what is its circumference?

   • A87.92 inches
   • B21.98 inches
   • C153.86 inches
   • D43.96 inches
   Antwort anzeigen

   Antwort: D. 43.96 inches

   Circumference = πd = 3.14 × 14 = 43.96 inches. Use the diameter, or 2 × the radius.

6. Frage 6 von 17

   A trapezoid has parallel sides of 8 feet and 12 feet and a height of 5 feet. What is its area?

   • A25 square feet
   • B50 square feet
   • C480 square feet
   • D100 square feet
   Antwort anzeigen

   Antwort: B. 50 square feet

   Area = 1/2 × h × (b₁ + b₂) = 1/2 × 5 × (8 + 12) = 50 square feet.

7. Frage 7 von 17

   A right triangle has legs of 9 inches and 12 inches. How long is the hypotenuse?

   • A15 inches
   • Babout 7.94 inches
   • C21 inches
   • D225 inches
   Antwort anzeigen

   Antwort: A. 15 inches

   Pythagorean theorem: a² + b² = c². 81 + 144 = 225, and √225 = 15 inches.

8. Frage 8 von 17

   A 13-foot ladder leans on a wall. Its base is 5 feet from the wall. How high up the wall does it reach?

   • Aabout 13.93 feet
   • B8 feet
   • C18 feet
   • D12 feet
   Antwort anzeigen

   Antwort: D. 12 feet

   The ladder is the hypotenuse: 5² + h² = 13², so h² = 169 − 25 = 144 and h = 12 feet.

9. Frage 9 von 17

   A rectangular patio is 20 feet by 12 feet. A 5-foot by 5-foot square in one corner is a planter, not paved. What area is paved?

   • A240 square feet
   • B215 square feet
   • C265 square feet
   • D230 square feet
   Antwort anzeigen

   Antwort: B. 215 square feet

   Whole patio: 20 × 12 = 240 square feet. Subtract the planter: 5 × 5 = 25. 240 − 25 = 215 square feet.

10. Frage 10 von 17

    A rectangle has an area of 84 square inches and a width of 7 inches. What is its length?

    • A35 inches
    • B588 inches
    • C77 inches
    • D12 inches
    Antwort anzeigen

    Antwort: D. 12 inches

    Area = length × width, so length = 84 ÷ 7 = 12 inches.

11. Frage 11 von 17

    A storage box is 2 feet by 3 feet by 4 feet. What is its volume?

    • A24 cubic feet
    • B52 cubic feet
    • C12 cubic feet
    • D9 cubic feet
    Antwort anzeigen

    Antwort: A. 24 cubic feet

    Volume of a rectangular prism = l × w × h = 2 × 3 × 4 = 24 cubic feet.

12. Frage 12 von 17

    How much paper is needed to cover all six faces of a box that is 2 feet by 3 feet by 4 feet?

    • A104 square feet
    • B26 square feet
    • C24 square feet
    • D52 square feet
    Antwort anzeigen

    Antwort: D. 52 square feet

    Surface area = 2(lw + lh + wh) = 2(6 + 8 + 12) = 2 × 26 = 52 square feet.

13. Frage 13 von 17

    A can is a cylinder with a radius of 3 inches and a height of 10 inches. Using π ≈ 3.14, what is its volume?

    • A282.6 cubic inches
    • B94.2 cubic inches
    • C1,130.4 cubic inches
    • D188.4 cubic inches
    Antwort anzeigen

    Antwort: A. 282.6 cubic inches

    Volume of a cylinder = πr²h = 3.14 × 9 × 10 = 282.6 cubic inches.

14. Frage 14 von 17

    A cone has a radius of 3 inches and a height of 8 inches. Using π ≈ 3.14, what is its volume?

    • A75.36 cubic inches
    • B25.12 cubic inches
    • C226.08 cubic inches
    • D150.72 cubic inches
    Antwort anzeigen

    Antwort: A. 75.36 cubic inches

    Volume of a cone = 1/3 × πr²h = 1/3 × 3.14 × 9 × 8 = 75.36 cubic inches. Without the 1/3 you would get 226.08.

15. Frage 15 von 17

    A pyramid has a square base 6 feet on each side and a height of 10 feet. What is its volume?

    • A180 cubic feet
    • B120 cubic feet
    • C20 cubic feet
    • D360 cubic feet
    Antwort anzeigen

    Antwort: B. 120 cubic feet

    Volume of a pyramid = 1/3 × base area × height = 1/3 × 36 × 10 = 120 cubic feet.

16. Frage 16 von 17

    A ball has a radius of 3 inches. Using π ≈ 3.14, what is its volume?

    • A37.68 cubic inches
    • B28.26 cubic inches
    • C113.04 cubic inches
    • D339.12 cubic inches
    Antwort anzeigen

    Antwort: C. 113.04 cubic inches

    Volume of a sphere = 4/3 × πr³ = 4/3 × 3.14 × 27 = 113.04 cubic inches.

17. Frage 17 von 17

    Each side of a cube-shaped box is doubled. What happens to the volume?

    • AIt becomes 8 times as large
    • BIt becomes 4 times as large
    • CIt doubles
    • DIt becomes 6 times as large
    Antwort anzeigen

    Antwort: A. It becomes 8 times as large

    Volume = s³. If s doubles, the volume is (2s)³ = 8s³, so it is 8 times as large.

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