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ASVAB Practice Test · Mathematics Knowledge

ASVAB Practice Test: Geometry Concepts

Importance ★★★★☆ · 45% (estimate)

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Written by AI. Only units that passed a separate AI check (re-reading facts and numbers) are published. Tell us if you find a mistake.

Overview

This chapter covers shapes and space. You will review angles, triangles, the perimeter and area of flat shapes, circles, and the volume of solid shapes. Most questions ask you to pick the right formula and do a short calculation.

Angles are measured in degrees. A right angle is 90 degrees, a straight line is 180 degrees, and two angles that add to 90 degrees are complementary while two that add to 180 degrees are supplementary. The three angles inside any triangle add up to 180 degrees.

In a right triangle, the Pythagorean theorem says a squared plus b squared equals c squared, where c is the longest side, the hypotenuse. Perimeter is the distance around a shape, and area is the space inside it. A rectangle's area is length times width, and a triangle's area is one-half times base times height.

For a circle, the radius goes from the center to the edge and the diameter is twice the radius. The circumference is pi times the diameter, and the area is pi times the radius squared. The volume of a box is length times width times height, and the volume of a cylinder is pi times the radius squared times the height.

Key concepts

  • Angle types

    Acute is less than 90 degrees, right is exactly 90, obtuse is between 90 and 180, and straight is 180. Complementary angles add to 90; supplementary angles add to 180.

    Memory tipComplementary = corner (90). Supplementary = straight (180).

  • Triangle angle sum

    The three inside angles of any triangle add up to 180 degrees. If two angles are 50 and 60, the third is 70.

    Memory tipSubtract the known angles from 180.

  • Pythagorean theorem

    In a right triangle, a^2 + b^2 = c^2, where c is the hypotenuse (the side across from the right angle). A 3-4-5 triangle is a common example.

    Memory tipRemember 3-4-5 and 5-12-13.

  • Area and perimeter

    Perimeter is the distance around a shape. Area is the space inside, in square units. Rectangle area = length x width. Triangle area = 1/2 x base x height.

    Memory tipPerimeter = fence. Area = carpet.

  • Circle formulas

    Diameter = 2 x radius. Circumference = pi x diameter (or 2 x pi x r). Area = pi x r^2. Pi is about 3.14.

    Memory tipArea uses r squared; circumference does not.

  • Volume

    The space inside a solid, in cubic units. Box (rectangular solid) = length x width x height. Cylinder = pi x r^2 x height. Cube = side^3.

    Memory tipVolume = base area x height.

Often tested

  • The angles of a triangle add up to 180 degrees.
  • Area of a circle = pi x r squared.
  • a^2 + b^2 = c^2 works only for right triangles.
  • The diameter is twice the radius.
  • Area uses square units; volume uses cubic units.

Easy to confuse: Circumference vs. area of a circle

MeasureWhat it meansFormula
CircumferenceDistance around the circlepi x diameter
AreaSpace inside the circlepi x radius squared

3 sample questions

Verified practice questions from this unit.

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°
▼ Show answer and explanation▲ Hide answer and explanation

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
▼ Show answer and explanation▲ Hide answer and explanation

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
▼ Show answer and explanation▲ Hide answer and explanation

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 5 questions from this unit →