GED Geometry Practice Questions, Set 2

This is set 2 of 2 for GED Geometry, with 22 practice questions that are not part of any full practice test. If a question type feels unfamiliar, review the Geometry study guide first, then check each answer below.

Question 1 of 22

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A circular walking path has a radius of 35 meters. About how far does a walker go in 4 laps? (Use π ≈ 3.14.)

Geometry practice set 2: 22 questions with answers

Work each question on paper first, then open the answer to check your reasoning.

  1. 1.A circular walking path has a radius of 35 meters. About how far does a walker go in 4 laps? (Use π ≈ 3.14.)

    1. A.About 440 meters
    2. B.About 879 meters
    3. C.About 1,758 meters
    4. D.About 3,846 meters
    Show answer

    Answer: B. About 879 meters

    One lap is 2πr = 2(3.14)(35) = 219.8 meters, and 4 laps is about 879 meters. Choice 440 meters uses πr, treating 35 meters as the diameter.

  1. 2.The angles of a triangle are in the ratio 2 : 3 : 4. What is the measure of the largest angle?

    1. A.40°
    2. B.60°
    3. C.90°
    4. D.80°
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    Answer: D. 80°

    The parts add to 9, so each part is 180 ÷ 9 = 20° and the largest angle is 4 × 20 = 80°. Choice 60° is the middle angle.

  1. 3.A rectangular yard is 3 times as long as it is wide. Its perimeter is 96 feet. What is its area?

    1. A.288 square feet
    2. B.432 square feet
    3. C.576 square feet
    4. D.96 square feet
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    Answer: B. 432 square feet

    The perimeter is 2(w + 3w) = 8w = 96, so w = 12 feet and the length is 36 feet. The area is 12 × 36 = 432 square feet. Choice 576 square feet comes from using 96 ÷ 4 = 24 as the width of a square.

  1. 4.A walkway 3 feet wide surrounds a rectangular pool that is 20 feet by 10 feet. What is the area of the walkway alone?

    1. A.416 square feet
    2. B.216 square feet
    3. C.180 square feet
    4. D.99 square feet
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    Answer: B. 216 square feet

    The pool plus walkway is (20 + 6) by (10 + 6), or 26 × 16 = 416 square feet. Subtract the pool’s 200 square feet to get 216. Choice 180 square feet multiplies the pool’s perimeter by 3 and leaves out the four corner squares.

  1. 5.A rectangular bulletin board has a perimeter of 22 feet and a width of 4 feet. What is its area?

    1. A.72 square feet
    2. B.88 square feet
    3. C.18 square feet
    4. D.28 square feet
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    Answer: D. 28 square feet

    Two lengths plus two widths make 22, so 2L + 8 = 22 and L = 7. The area is 7 × 4 = 28 square feet. Choice 88 multiplies the perimeter by the width.

  1. 6.A triangular sail has an area of 54 square feet and a base of 9 feet. What is the height of the sail?

    1. A.24 feet
    2. B.45 feet
    3. C.12 feet
    4. D.6 feet
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    Answer: C. 12 feet

    Use A = ½bh: 54 = ½ × 9 × h, so 54 = 4.5h and h = 12 feet. Choice 6 feet divides 54 by 9 and forgets the ½.

  1. 7.A softball field’s infield is a square 60 feet on each side. To the nearest foot, what is the straight-line distance from one corner of the square to the opposite corner?

    1. A.72 feet
    2. B.60 feet
    3. C.85 feet
    4. D.120 feet
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    Answer: C. 85 feet

    The diagonal is the hypotenuse of a right triangle with legs of 60 feet: √(60² + 60²) = √7,200 ≈ 84.9, or 85 feet. Choice 120 feet adds the two legs.

  1. 8.Which set of side lengths forms a right triangle?

    1. A.6, 9, 12
    2. B.7, 10, 12
    3. C.5, 11, 13
    4. D.8, 15, 17
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    Answer: D. 8, 15, 17

    8² + 15² = 64 + 225 = 289 = 17², so these sides fit the Pythagorean theorem. For 6, 9, 12, the sum 36 + 81 = 117 does not equal 144.

  1. 9.A rectangular yard is 50 feet by 30 feet. A circular pond with a radius of 6 feet sits in the yard. To the nearest square foot, how much of the yard is lawn? (Use π ≈ 3.14.)

    1. A.1,048 square feet
    2. B.1,462 square feet
    3. C.1,613 square feet
    4. D.1,387 square feet
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    Answer: D. 1,387 square feet

    The yard is 50 × 30 = 1,500 square feet and the pond is 3.14 × 6² ≈ 113 square feet, leaving about 1,387. Choice 1,462 subtracts 2πr, the pond’s circumference, instead of its area.

  1. 10.A parking lot is shaped like a trapezoid with parallel sides of 80 meters and 120 meters that are 50 meters apart. A rectangular strip 120 meters by 10 meters is added along the 120-meter side. What is the total area?

    1. A.6,000 square meters
    2. B.5,000 square meters
    3. C.6,200 square meters
    4. D.11,200 square meters
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    Answer: C. 6,200 square meters

    The trapezoid is ½ × (80 + 120) × 50 = 5,000 square meters and the strip is 120 × 10 = 1,200, for 6,200 in all. Choice 11,200 forgets the ½ in the trapezoid formula.

  1. 11.A lawn sprinkler waters a circle with a radius of 15 feet. The radius is turned down to 12 feet. To the nearest square foot, how much less area does it water? (Use π ≈ 3.14.)

    1. A.254 square feet
    2. B.28 square feet
    3. C.19 square feet
    4. D.452 square feet
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    Answer: A. 254 square feet

    The area drops from 3.14 × 225 to 3.14 × 144, a difference of 3.14 × 81 ≈ 254 square feet. Choice 28 square feet squares the 3-foot change in radius, which is not the same as subtracting the two areas.

  1. 12.What is the sum of the interior angles of an octagon?

    1. A.135°
    2. B.900°
    3. C.1,440°
    4. D.1,080°
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    Answer: D. 1,080°

    The sum is (n − 2) × 180° = 6 × 180° = 1,080°. Choice 135° is the measure of one angle in a regular octagon, not the sum.

  1. 13.A paper label wraps once around the side of a can, with no overlap and nothing on the top or bottom. The can has a radius of 1.5 inches and a height of 4 inches. To the nearest tenth, what is the area of the label? (Use π ≈ 3.14.)

    1. A.37.7 square inches
    2. B.18.8 square inches
    3. C.28.3 square inches
    4. D.51.8 square inches
    Show answer

    Answer: A. 37.7 square inches

    The side of a cylinder unrolls into a rectangle 2πr long and h tall: 2 × 3.14 × 1.5 × 4 = 37.68, about 37.7 square inches. Choice 51.8 also includes the top and bottom circles.

  1. 14.A 4-inch by 6-inch photo is enlarged so that the short side becomes 10 inches. How long is the long side of the enlargement?

    1. A.12 inches
    2. B.15 inches
    3. C.24 inches
    4. D.60 inches
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    Answer: B. 15 inches

    The scale factor is 10 ÷ 4 = 2.5, so the long side is 6 × 2.5 = 15 inches. Choice 12 inches adds 6 to the long side instead of multiplying.

  1. 15.Two rectangles are similar. The larger one’s sides are 3 times the smaller one’s. The smaller rectangle has an area of 15 square inches. What is the area of the larger one?

    1. A.45 square inches
    2. B.405 square inches
    3. C.18 square inches
    4. D.135 square inches
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    Answer: D. 135 square inches

    Area grows by the square of the scale factor: 15 × 3² = 135. Choice 45 multiplies the area by 3, which only works for lengths.

  1. 16.A stage is a 12 ft by 8 ft rectangle with a semicircle attached to one 8-foot side. The semicircle’s diameter is 8 feet. What is the stage’s area, to the nearest tenth? (Use π ≈ 3.14.)

    1. A.121.1 sq ft
    2. B.196.5 sq ft
    3. C.108.6 sq ft
    4. D.146.2 sq ft
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    Answer: A. 121.1 sq ft

    The rectangle is 96. The semicircle has radius 4, so its area is ½ × 3.14 × 16 = 25.12. The total is about 121.1. Choice 146.2 adds a full circle instead of half.

  1. 17.A square metal plate is 10 inches on each side. A circular hole with a radius of 3 inches is cut out. What area of metal is left? (Use π ≈ 3.14.)

    1. A.71.74 sq in
    2. B.81.16 sq in
    3. C.90.58 sq in
    4. D.128.26 sq in
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    Answer: A. 71.74 sq in

    The square is 100 and the hole is 3.14 × 3² = 28.26, so 100 − 28.26 = 71.74. Choice 81.16 subtracts 2πr, the hole’s circumference, instead of its area.

  1. 18.On a coordinate grid, what is the distance between (−1, 2) and (5, 10)?

    1. A.12
    2. B.10
    3. C.7
    4. D.14
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    Answer: B. 10

    The horizontal change is 6 and the vertical change is 8, so the distance is √(36 + 64) = √100 = 10. Choice 14 adds 6 and 8.

  1. 19.A support cable runs from the top of a 40-foot radio tower to a stake in the ground 9 feet from the base of the tower. How long is the cable?

    1. A.49 feet
    2. B.39 feet
    3. C.41 feet
    4. D.31 feet
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    Answer: C. 41 feet

    The cable is the hypotenuse: 40² + 9² = 1,600 + 81 = 1,681, and √1,681 = 41. Choice 49 feet adds the two lengths instead of using the Pythagorean theorem.

  1. 20.A can has a radius of 3 cm and a height of 10 cm. What is its total surface area, including the top and bottom? (Use π ≈ 3.14.)

    1. A.about 216.7 sq cm
    2. B.about 244.9 sq cm
    3. C.about 282.6 sq cm
    4. D.about 188.4 sq cm
    Show answer

    Answer: B. about 244.9 sq cm

    Two circles: 2 × 3.14 × 9 = 56.52. The side: 2 × 3.14 × 3 × 10 = 188.4. Total ≈ 244.9. Choice 188.4 is the side only, and 282.6 is the volume.

  1. 21.All six faces of a cube-shaped storage box are painted. Each edge is 5 feet long. What area is painted?

    1. A.125 square feet
    2. B.25 square feet
    3. C.150 square feet
    4. D.100 square feet
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    Answer: C. 150 square feet

    Each face is 5 × 5 = 25 square feet and there are 6 faces, so 6 × 25 = 150. Choice 125 is the volume, 5³.

  1. 22.A fish tank is 30 inches long, 12 inches wide, and 15 inches tall. One gallon is 231 cubic inches. About how many gallons does the tank hold?

    1. A.23.4 gallons
    2. B.5,400 gallons
    3. C.2.3 gallons
    4. D.14.5 gallons
    Show answer

    Answer: A. 23.4 gallons

    Volume is 30 × 12 × 15 = 5,400 cubic inches, and 5,400 ÷ 231 ≈ 23.4 gallons. Choice 5,400 is the volume in cubic inches, not gallons.

More practice sets

Geometry has 2 practice sets. None of these questions appear in the full practice tests.