ASVAB Mathematics: Geometry and Measurement — Questions and Answers

Question 1: What is the area of a rectangle with length 12 cm and width 5 cm?

34 cm²
60 cm² (Correct answer)
17 cm²
70 cm²

Correct answer: 60 cm²

Area = length × width = 12 × 5 = 60 cm².

The formula for the area of a rectangle is A = l × w. Substituting: A = 12 × 5 = 60 cm².

Question 2: What is the perimeter of a square with a side length of 7 meters?

14 m
28 m (Correct answer)
49 m
21 m

Correct answer: 28 m

Perimeter of a square = 4 × side = 4 × 7 = 28 m.

A square has four equal sides. Perimeter = 4 × s = 4 × 7 = 28 meters.

Question 3: What is the area of a triangle with base 10 cm and height 6 cm?

60 cm²
30 cm² (Correct answer)
16 cm²
120 cm²

Correct answer: 30 cm²

Area = ½ × base × height = ½ × 10 × 6 = 30 cm².

The area of a triangle is A = ½ × b × h. Substituting: A = ½ × 10 × 6 = 30 cm².

Question 4: What is the circumference of a circle with diameter 14 cm? (Use π ≈ 3.14)

43.96 cm (Correct answer)
153.86 cm
21.98 cm
28 cm

Correct answer: 43.96 cm

C = π × d = 3.14 × 14 = 43.96 cm.

Circumference = π × d = 3.14 × 14 = 43.96 cm. Alternatively, C = 2πr where r = 7: 2 × 3.14 × 7 = 43.96 cm.

Question 5: A right triangle has legs of 3 and 4. What is the hypotenuse?

5 (Correct answer)
7
6
√7

Correct answer: 5

Pythagorean theorem: c² = a² + b² = 9 + 16 = 25; c = 5.

The Pythagorean theorem states c² = a² + b². c² = 3² + 4² = 9 + 16 = 25. c = √25 = 5. The 3-4-5 right triangle is a common benchmark.

Question 6: What is the volume of a rectangular box that is 4 m × 3 m × 2 m?

18 m³
24 m³ (Correct answer)
26 m³
48 m³

Correct answer: 24 m³

Volume = length × width × height = 4 × 3 × 2 = 24 m³.

Volume of a rectangular prism (box) = l × w × h = 4 × 3 × 2 = 24 m³.

Question 7: How many degrees are in a straight line (straight angle)?

90°
270°
360°
180° (Correct answer)

Correct answer: 180°

A straight angle measures exactly 180 degrees.

A straight angle is formed when two rays point in exactly opposite directions, forming a straight line. It measures 180°. A right angle = 90°, a full circle = 360°.

Question 8: What is the area of a circle with radius 5 cm? (Use π ≈ 3.14)

31.4 cm²
78.5 cm² (Correct answer)
15.7 cm²
62.8 cm²

Correct answer: 78.5 cm²

Area = π × r² = 3.14 × 25 = 78.5 cm².

Area of a circle = πr² = 3.14 × 5² = 3.14 × 25 = 78.5 cm².

Question 9: What is the sum of interior angles of a triangle?

90°
270°
180° (Correct answer)
360°

Correct answer: 180°

The sum of the interior angles of any triangle is always 180°.

The interior angles of any triangle always sum to 180°. For example, a right triangle has one 90° angle; the other two must add to 90°. An equilateral triangle has three 60° angles: 60 + 60 + 60 = 180.

Question 10: What does 'perimeter' measure?

The space inside a shape
The total distance around the outside of a shape (Correct answer)
The height of a shape
The diagonal length

Correct answer: The total distance around the outside of a shape

Perimeter is the total length of all sides around the boundary of a shape.

Perimeter is the total distance around the outer boundary of a two-dimensional shape. It is found by adding the lengths of all sides. Units are linear (cm, m, ft).

Question 11: A rectangle has a perimeter of 36 cm and a width of 6 cm. What is its length?

12 cm (Correct answer)
14 cm
15 cm
24 cm

Correct answer: 12 cm

P = 2(l + w); 36 = 2(l + 6); 18 = l + 6; l = 12 cm.

Perimeter = 2(l + w). Substitute: 36 = 2(l + 6). Divide by 2: 18 = l + 6. Subtract 6: l = 12 cm.

Question 12: What is the volume of a cylinder with radius 3 cm and height 10 cm? (Use π ≈ 3.14)

94.2 cm³
282.6 cm³ (Correct answer)
188.4 cm³
942 cm³

Correct answer: 282.6 cm³

V = π × r² × h = 3.14 × 9 × 10 = 282.6 cm³.

Volume of a cylinder = πr²h = 3.14 × 3² × 10 = 3.14 × 9 × 10 = 282.6 cm³.

Question 13: What type of angle is greater than 90° but less than 180°?

Acute
Right
Obtuse (Correct answer)
Reflex

Correct answer: Obtuse

An obtuse angle measures between 90° and 180°.

Angles are classified by size: acute (< 90°), right (= 90°), obtuse (90°–180°), straight (= 180°), and reflex (> 180°). An angle of 120° is obtuse.

Question 14: How many feet are in one yard?

2
3 (Correct answer)
4
12

Correct answer: 3

1 yard = 3 feet.

The US customary system: 1 yard = 3 feet; 1 foot = 12 inches. Therefore, 1 yard = 36 inches.

Question 15: What is the perimeter of a triangle with sides 5 cm, 7 cm, and 9 cm?

16 cm
21 cm (Correct answer)
14 cm
63 cm

Correct answer: 21 cm

Perimeter = 5 + 7 + 9 = 21 cm.

The perimeter of a triangle is found by adding all three side lengths: 5 + 7 + 9 = 21 cm.

Question 16: What is the surface area of a cube with side length 4 cm?

16 cm²
64 cm²
96 cm² (Correct answer)
48 cm²

Correct answer: 96 cm²

Surface area = 6 × s² = 6 × 16 = 96 cm².

A cube has 6 faces, each a square with area s². Total surface area = 6s² = 6 × 4² = 6 × 16 = 96 cm².

Question 17: Convert 5 kilometers to meters.

500 m
5,000 m (Correct answer)
50 m
50,000 m

Correct answer: 5,000 m

1 km = 1,000 m; 5 km = 5,000 m.

The prefix 'kilo' means 1,000. Therefore, 1 kilometer = 1,000 meters. 5 km × 1,000 m/km = 5,000 meters.

Question 18: Two angles are supplementary. One measures 65°. What is the other?

25°
115° (Correct answer)
125°
95°

Correct answer: 115°

Supplementary angles add to 180°. 180° - 65° = 115°.

Supplementary angles together form a straight angle (180°). If one angle is 65°, the supplement is 180° - 65° = 115°. Compare with complementary angles, which sum to 90°.

Question 19: What is the area of a parallelogram with base 8 m and height 5 m?

13 m²
40 m² (Correct answer)
26 m²
80 m²

Correct answer: 40 m²

Area of a parallelogram = base × height = 8 × 5 = 40 m².

The area of a parallelogram = b × h = 8 × 5 = 40 m². The height must be perpendicular to the base (not the slant side).

Question 20: A ladder 13 feet long leans against a wall. The base of the ladder is 5 feet from the wall. How high does it reach?

8 ft
10 ft
12 ft (Correct answer)
11 ft

Correct answer: 12 ft

c² = a² + b²; 13² = 5² + h²; 169 = 25 + h²; h² = 144; h = 12 ft.

The ladder (hypotenuse = 13), the distance from the wall (leg = 5), and the height on the wall (unknown leg) form a right triangle. 13² = 5² + h²; 169 - 25 = 144; h = √144 = 12 feet.

Question 21: What is the volume of a sphere with radius 3 cm? (Use π ≈ 3.14)

37.68 cm³
113.04 cm³ (Correct answer)
75.36 cm³
339.12 cm³

Correct answer: 113.04 cm³

V = (4/3) × π × r³ = (4/3) × 3.14 × 27 = 113.04 cm³.

Volume of a sphere = (4/3)πr³ = (4/3) × 3.14 × 3³ = (4/3) × 3.14 × 27 = (4 × 3.14 × 27) / 3 = 339.12 / 3 = 113.04 cm³.

Question 22: How many centimeters are in one meter?

10
100 (Correct answer)
1000
0.1

Correct answer: 100

1 meter = 100 centimeters.

In the metric system, 'centi' means 1/100. Therefore, 1 meter = 100 centimeters. To convert meters to centimeters, multiply by 100.

Question 23: What is the diagonal of a rectangle with length 8 and width 6?

10 (Correct answer)
14
7
√28

Correct answer: 10

d = √(l² + w²) = √(64 + 36) = √100 = 10.

The diagonal of a rectangle divides it into two right triangles. Using Pythagorean theorem: d² = 8² + 6² = 64 + 36 = 100. d = √100 = 10.

Question 24: What is the measure of each interior angle of a regular hexagon?

60°
90°
120° (Correct answer)
108°

Correct answer: 120°

Sum of interior angles = (6-2) × 180 = 720°. Each = 720°/6 = 120°.

For any polygon with n sides, the sum of interior angles = (n-2) × 180°. For a hexagon: (6-2) × 180 = 4 × 180 = 720°. Each angle in a regular hexagon = 720°/6 = 120°.

Question 25: Convert 2.5 miles to feet. (1 mile = 5,280 feet)

10,560 ft
13,200 ft (Correct answer)
7,920 ft
5,280 ft

Correct answer: 13,200 ft

2.5 × 5,280 = 13,200 feet.

1 mile = 5,280 feet. 2.5 miles × 5,280 ft/mile = 13,200 feet.

Question 26: A rectangular room is 15 ft × 12 ft. How many square feet of carpet are needed?

54 ft²
180 ft² (Correct answer)
27 ft²
144 ft²

Correct answer: 180 ft²

Area = 15 × 12 = 180 ft².

Area of a rectangle = l × w = 15 × 12 = 180 square feet. This represents the floor area requiring carpet.

Question 27: What is the relationship between radius and diameter of a circle?

Diameter = radius + 2
Diameter = 2 × radius (Correct answer)
Radius = 2 × diameter
They are equal

Correct answer: Diameter = 2 × radius

The diameter is twice the radius (d = 2r).

The radius is the distance from the center of a circle to any point on its circumference. The diameter passes through the center, connecting two points on the circumference. Therefore, diameter = 2 × radius.

Question 28: What is the area of a trapezoid with parallel sides of 8 and 12 and a height of 5?

25
40
50 (Correct answer)
100

Correct answer: 50

Area = ½(b₁ + b₂) × h = ½(8 + 12) × 5 = ½ × 20 × 5 = 50.

Area of a trapezoid = ½(b₁ + b₂) × h = ½(8 + 12) × 5 = ½ × 20 × 5 = 50 square units.

Question 29: An angle and its complement are in a 2:1 ratio. What is the larger angle?

30°
45°
60° (Correct answer)
120°

Correct answer: 60°

Complementary angles sum to 90°. Ratio 2:1 means angles are 60° and 30°.

Complementary angles sum to 90°. Let the angles be 2x and x. 2x + x = 90; 3x = 90; x = 30. The larger angle = 2x = 60°.

Question 30: What is the total surface area of a rectangular prism that is 6 cm × 4 cm × 3 cm?

72 cm²
108 cm² (Correct answer)
144 cm²
216 cm²

Correct answer: 108 cm²

SA = 2(lw + lh + wh) = 2(24 + 18 + 12) = 2(54) = 108 cm².

Surface area of a rectangular prism = 2(lw + lh + wh). Substituting: 2(6×4 + 6×3 + 4×3) = 2(24 + 18 + 12) = 2(54) = 108 cm².

Question 31: How many inches are in 3 feet?

24 inches
36 inches (Correct answer)
30 inches
48 inches

Correct answer: 36 inches

1 foot = 12 inches; 3 × 12 = 36 inches.

There are 12 inches in 1 foot. Therefore, 3 feet = 3 × 12 = 36 inches.

Question 32: What is the name of a polygon with 8 sides?

Hexagon
Heptagon
Octagon (Correct answer)
Decagon

Correct answer: Octagon

An octagon has 8 sides. The prefix 'octo' means eight.

Polygon sides: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8), nonagon (9), decagon (10). 'Octo' is Latin for eight.

Question 33: What is the scale if 1 inch on a map represents 50 miles in reality?

1:50 (Correct answer)
1:50,000
1:500
1:63,360

Correct answer: 1:50

The scale is 1 inch = 50 miles, typically written as 1:50 in map terms (depending on units).

A map scale shows the ratio of map distance to real distance. If the problem states 1 inch represents 50 miles, the ratio scale in consistent units would be 1:3,168,000 (converting miles to inches), but as expressed in the answer choices in the map's stated ratio, the answer is 1:50 (miles).

Question 34: Two parallel lines are cut by a transversal. What is the relationship between alternate interior angles?

They are supplementary
They are complementary
They are equal (congruent) (Correct answer)
They add up to 90°

Correct answer: They are equal (congruent)

Alternate interior angles formed by parallel lines and a transversal are always equal.

When a transversal crosses two parallel lines, alternate interior angles (on opposite sides of the transversal, between the parallel lines) are congruent (equal in measure). This is a fundamental theorem in Euclidean geometry.

Question 35: What is the distance formula between points (1, 2) and (4, 6)?

3
4
5 (Correct answer)
7

Correct answer: 5

d = √[(4-1)² + (6-2)²] = √[9 + 16] = √25 = 5.

Distance formula: d = √[(x₂-x₁)² + (y₂-y₁)²] = √[(4-1)² + (6-2)²] = √[3² + 4²] = √[9+16] = √25 = 5.

ASVAB Mathematics: Geometry and Measurement

What is the area of a rectangle with length 12 cm and width 5 cm?

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