IMSA Geometry and Spatial Reasoning 2 — Questions and Answers
Question 1: In a right triangle, one leg is 8 and the hypotenuse is 10. What is the other leg?
- 6 (Correct answer)
- 7
- 4
- 9
Correct answer: 6
By the Pythagorean theorem: 8² + b² = 10², so 64 + b² = 100, giving b = 6.
Question 2: What is the area of a circle with diameter 12? (Use π ≈ 3.14)
- 113.04 (Correct answer)
- 75.36
- 452.16
- 37.68
Correct answer: 113.04
Radius = 6; Area = πr² = 3.14 × 36 = 113.04.
Question 3: Two parallel lines are cut by a transversal. Alternate interior angles are:
- Equal (Correct answer)
- Supplementary
- Complementary
- Adjacent
Correct answer: Equal
When a transversal cuts parallel lines, alternate interior angles are always equal.
Question 4: A square has an area of 81 cm². What is its perimeter?
- 36 cm (Correct answer)
- 18 cm
- 27 cm
- 324 cm
Correct answer: 36 cm
Side = √81 = 9 cm; Perimeter = 4 × 9 = 36 cm.
Question 5: What is the measure of each interior angle of a regular pentagon?
- 108° (Correct answer)
- 72°
- 120°
- 90°
Correct answer: 108°
Sum of interior angles = (5-2) × 180° = 540°; each angle = 540°/5 = 108°.
Question 6: A cylinder has radius 3 and height 5. What is its volume? (Use π ≈ 3.14)
- 141.3 (Correct answer)
- 188.4
- 94.2
- 47.1
Correct answer: 141.3
Volume = πr²h = 3.14 × 9 × 5 = 141.3.
IMSA Geometry and Spatial Reasoning 2
In a right triangle, one leg is 8 and the hypotenuse is 10.
What is the other leg?