AMC 8 Geometry & Measurement 2 — Questions and Answers
Question 1: What is the volume of a rectangular box with dimensions 3 × 4 × 5?
- 47
- 60 (Correct answer)
- 80
- 94
Correct answer: 60
Volume = length × width × height = 3 × 4 × 5 = 60 cubic units.
Question 2: In a right triangle, the two legs are 5 and 12. What is the length of the hypotenuse?
- 11
- 13 (Correct answer)
- 15
- 17
Correct answer: 13
By the Pythagorean theorem, hypotenuse = √(5² + 12²) = √(25 + 144) = √169 = 13.
Question 3: A trapezoid has parallel bases of length 6 and 10, and a height of 4. What is its area?
- 24
- 32 (Correct answer)
- 40
- 64
Correct answer: 32
Area = ½ × (b₁ + b₂) × h = ½ × (6 + 10) × 4 = 32.
Question 4: Two supplementary angles are in the ratio 2:7. What is the measure of the larger angle?
- 40°
- 70°
- 120°
- 140° (Correct answer)
Correct answer: 140°
Let the angles be 2x and 7x; then 2x + 7x = 180°, giving x = 20°, so the larger angle = 7 × 20° = 140°.
Question 5: How many degrees are there in the sum of the interior angles of a pentagon?
- 360°
- 450°
- 540° (Correct answer)
- 720°
Correct answer: 540°
The interior angle sum of a pentagon = (5−2) × 180° = 3 × 180° = 540°.
Question 6: A right triangle has one leg of length 8 and hypotenuse of length 10. What is the area of the triangle?
- 24 (Correct answer)
- 30
- 40
- 48
Correct answer: 24
The other leg = √(10² − 8²) = √(100 − 64) = √36 = 6, so area = ½ × 8 × 6 = 24.
AMC 8 Geometry & Measurement 2
What is the volume of a rectangular box with dimensions 3 × 4 × 5?