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ASVAB Practice Test · Mathematics Knowledge

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ASVAB Practice Test Geometry Summary

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★★★★☆ (4 / 5)
Weight
About 7 of 15 Mathematics Knowledge questions (45%)

Angles, triangles, area, perimeter, volume, and circles.

📖 See Geometry concepts →

Geometry: must-know points

  • The angles of a triangle add up to 180 degrees.
  • Area of a circle = pi x r squared.

Geometry: 8 sample questions

Practice questionReviewedMathematics Knowledge › Geometry★★★★☆

Question 1. Two angles of a triangle measure 50° and 60°. What is the measure of the third angle?

  1. ① 80°
  2. ② 90°
  3. ③ 70°
  4. ④ 110°
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Answer: ③ 70°

Key point: Triangle angles add up to 180°

  1. The angles of a triangle add up to 180°.
  2. 50 + 60 = 110.
  3. 180 - 110 = 70°.

Check: 50 + 60 + 70 = 180.

Wrong choices

  • (A) 80°: 80° gives a total of 190°.
  • (B) 90°: 90° gives a total of 200°.
  • (D) 110°: 110° is the sum of the two given angles.
Practice questionReviewedMathematics Knowledge › Geometry★★★★☆

Question 2. A rectangular floor mat is 8 feet long and 5 feet wide. What is its area?

  1. ① 40 square feet
  2. ② 26 square feet
  3. ③ 13 square feet
  4. ④ 80 square feet
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Answer: ① 40 square feet

Key point: Rectangle area = length x width

  1. Area of a rectangle = length x width.
  2. 8 x 5 = 40 square feet.

Check: 40 / 8 = 5 feet wide.

Wrong choices

  • (B) 26 square feet: 26 is the perimeter (8 + 5 + 8 + 5), not the area.
  • (C) 13 square feet: 13 just adds the length and width.
  • (D) 80 square feet: 80 doubles the correct area.
Practice questionReviewedMathematics Knowledge › Geometry★★★★☆

Question 3. What is the perimeter of a square with sides 7 inches long?

  1. ① 28 inches
  2. ② 21 inches
  3. ③ 14 inches
  4. ④ 49 inches
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Answer: ① 28 inches

Key point: Square perimeter = 4 x side

  1. A square has 4 equal sides.
  2. Perimeter = 4 x 7 = 28 inches.

Check: 7 + 7 + 7 + 7 = 28.

Wrong choices

  • (B) 21 inches: 21 counts only 3 sides.
  • (C) 14 inches: 14 counts only 2 sides.
  • (D) 49 inches: 49 is the area (7 x 7), not the perimeter.
Practice questionReviewedMathematics Knowledge › Geometry★★★★☆

Question 4. What is the area of a circle with a radius of 5 inches? (Leave the answer in terms of π.)

  1. ① 100π square inches
  2. ② 10π square inches
  3. ③ 25π square inches
  4. ④ 5π square inches
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Answer: ③ 25π square inches

Key point: Circle area = π x r²

  1. Area of a circle = π x r².
  2. r² = 5 x 5 = 25.
  3. Area = 25π square inches.

Check: about 3.14 x 25 = 78.5 square inches.

Wrong choices

  • (A) 100π square inches: 100π squares the diameter (10) instead of the radius.
  • (B) 10π square inches: 10π is the circumference (2 x π x 5), not the area.
  • (D) 5π square inches: 5π leaves out squaring the radius.
Practice questionReviewedMathematics Knowledge › Geometry★★★★☆

Question 5. A right triangle has legs 6 feet and 8 feet long. How long is the hypotenuse?

  1. ① 7 feet
  2. ② 12 feet
  3. ③ 14 feet
  4. ④ 10 feet
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Answer: ④ 10 feet

Key point: Pythagorean theorem: a² + b² = c²

  1. Use a² + b² = c².
  2. 6² + 8² = 36 + 64 = 100.
  3. c = √100 = 10 feet.

Check: 10² = 100 = 36 + 64.

Wrong choices

  • (A) 7 feet: 7 is the average of the legs, but the hypotenuse must be the longest side.
  • (B) 12 feet: 12 squared is 144, not 100.
  • (C) 14 feet: 14 adds the two legs; the hypotenuse is shorter than the two legs together.
Practice questionReviewedMathematics Knowledge › Geometry★★★★☆

Question 6. How many degrees are in a right angle?

  1. ① 360°
  2. ② 90°
  3. ③ 180°
  4. ④ 45°
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Answer: ② 90°

Key point: A right angle is 90°

A right angle is a square corner, like the corner of a sheet of paper. It measures exactly 90 degrees.

Wrong choices

  • (A) 360°: 360° is a full circle.
  • (C) 180°: 180° is a straight angle, a straight line.
  • (D) 45°: 45° is half of a right angle.
Practice questionReviewedMathematics Knowledge › Geometry★★★★☆

Question 7. A storage box is 4 feet long, 3 feet wide, and 2 feet high. What is its volume?

  1. ① 12 cubic feet
  2. ② 52 cubic feet
  3. ③ 24 cubic feet
  4. ④ 9 cubic feet
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Answer: ③ 24 cubic feet

Key point: Box volume = length x width x height

  1. Volume = length x width x height.
  2. 4 x 3 x 2 = 24 cubic feet.

Check: the bottom is 4 x 3 = 12 square feet, and 2 layers of 12 = 24.

Wrong choices

  • (A) 12 cubic feet: 12 is only the area of the bottom, without the height.
  • (B) 52 cubic feet: 52 is the surface area: 2(4x3 + 4x2 + 3x2) = 2(26) = 52 square feet.
  • (D) 9 cubic feet: 9 adds the three measurements instead of multiplying.
Practice questionReviewedMathematics Knowledge › Geometry★★★★☆

Question 8. The circumference of a circle is 12π inches. What is the area of the circle?

  1. ① 12π square inches
  2. ② 36π square inches
  3. ③ 144π square inches
  4. ④ 24π square inches
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Answer: ② 36π square inches

Key point: Find the radius from C = 2πr first

  1. Circumference = 2πr, so 2πr = 12π.
  2. Divide by 2π: r = 6 inches.
  3. Area = πr² = π x 36 = 36π square inches.

Check: with r = 6, circumference = 2 x π x 6 = 12π.

Wrong choices

  • (A) 12π square inches: 12π is the circumference, not the area.
  • (C) 144π square inches: 144π uses 12 as the radius, but 12 is the diameter; the radius is 6.
  • (D) 24π square inches: 24π uses 2 x π x 12, a circumference formula with the wrong radius, not the area.

Test yourself.

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