PSAT/NMSQT Geometry & Measurement 3 — Questions and Answers
Question 1: Triangle ABC is similar to triangle DEF. If AB = 4, DE = 12, and BC = 6, what is EF?
- 18 (Correct answer)
- 14
- 8
- 24
Correct answer: 18
The scale factor is 12/4 = 3, so EF = 6 × 3 = 18.
Question 2: What is the area of a circle with radius 3? (Use π.)
- 9π (Correct answer)
- 6π
- 3π
- 12π
Correct answer: 9π
Area = πr² = π × 3² = 9π.
Question 3: A cylinder has radius 2 and height 5. What is its volume? (Use π.)
- 20π (Correct answer)
- 10π
- 40π
- 25π
Correct answer: 20π
Volume = πr²h = π × 4 × 5 = 20π.
Question 4: A 30-60-90 triangle has its shortest side equal to 5. What is the hypotenuse?
- 10 (Correct answer)
- 5√3
- 5√2
- 15
Correct answer: 10
In a 30-60-90 triangle the hypotenuse is twice the shortest side, so 2 × 5 = 10.
Question 5: The sum of the interior angles of a pentagon is what?
- 540° (Correct answer)
- 360°
- 720°
- 450°
Correct answer: 540°
Interior angle sum = (n − 2) × 180° = 3 × 180° = 540°.
Question 6: Two parallel lines are cut by a transversal. If one angle is 70°, what is its corresponding angle?
- 70° (Correct answer)
- 110°
- 20°
- 90°
Correct answer: 70°
Corresponding angles formed by parallel lines are congruent, so it is 70°.
Question 7: What is the surface area of a cube with edge length 3?
- 54 (Correct answer)
- 27
- 36
- 18
Correct answer: 54
Surface area = 6s² = 6 × 9 = 54.
PSAT/NMSQT Geometry & Measurement 3
Triangle ABC is similar to triangle DEF.
If AB = 4, DE = 12, and BC = 6, what is EF?