AST Geometry and Trigonometry 1 — Questions and Answers
Question 1: What is the area of a circle with radius 6?
- 12π
- 36π (Correct answer)
- 6π²
- 18π
Correct answer: 36π
The area of a circle is πr², so π(6)² = 36π.
Question 2: What is the sum of the interior angles of a pentagon?
- 360°
- 540° (Correct answer)
- 720°
- 450°
Correct answer: 540°
The sum of interior angles of an n-sided polygon is (n−2)×180°, so (5−2)×180° = 540°.
Question 3: A right triangle has legs of length 3 and 4. What is the length of the hypotenuse?
- 7
- 5 (Correct answer)
- 6
- √7
Correct answer: 5
By the Pythagorean theorem, c = √(3² + 4²) = √(9 + 16) = √25 = 5.
Question 4: What is the area of a triangle with base 10 and height 6?
- 60
- 30 (Correct answer)
- 16
- 15
Correct answer: 30
The area of a triangle is ½ × base × height = ½ × 10 × 6 = 30.
Question 5: Two parallel lines are cut by a transversal. Which pair of angles is supplementary?
- Vertical angles
- Corresponding angles
- Co-interior (same-side interior) angles (Correct answer)
- Alternate interior angles
Correct answer: Co-interior (same-side interior) angles
Co-interior (same-side interior) angles add up to 180° when formed by parallel lines and a transversal.
Question 6: What is the volume of a cube with side length 4?
- 16
- 24
- 64 (Correct answer)
- 48
Correct answer: 64
The volume of a cube is s³ = 4³ = 64.
Question 7: A rectangle has a perimeter of 36 and a width of 6. What is its length?
- 12 (Correct answer)
- 6
- 24
- 9
Correct answer: 12
Using P = 2L + 2W: 36 = 2L + 12, so 2L = 24 and L = 12.
AST Geometry and Trigonometry 1
What is the area of a circle with radius 6?