AMC 8 Geometry & Measurement 3 — Questions and Answers
Question 1: A square is inscribed in a circle of radius 5. What is the area of the square?
- 25
- 50 (Correct answer)
- 75
- 100
Correct answer: 50
The diagonal of the inscribed square equals the diameter (10), so s√2 = 10, giving s = 5√2 and area = s² = 50.
Question 2: How many lines of symmetry does a regular pentagon have?
- 3
- 4
- 5 (Correct answer)
- 6
Correct answer: 5
A regular pentagon has 5 lines of symmetry, one through each vertex and the midpoint of the opposite side.
Question 3: A rectangle's length is three times its width. If the perimeter is 48, what is the area?
- 72
- 108 (Correct answer)
- 144
- 180
Correct answer: 108
With l = 3w, the perimeter gives 2(3w + w) = 48, so w = 6, l = 18, and area = 108.
Question 4: In a right triangle, one acute angle is 35°. What is the other acute angle?
- 45°
- 55° (Correct answer)
- 65°
- 75°
Correct answer: 55°
The two acute angles in a right triangle are complementary, so the other angle = 90° − 35° = 55°.
Question 5: What is the perimeter of a regular octagon with side length 7?
- 42
- 49
- 56 (Correct answer)
- 64
Correct answer: 56
A regular octagon has 8 equal sides, so perimeter = 8 × 7 = 56.
Question 6: A cylinder has radius 3 and height 7. What is its volume? (Use π ≈ 3.14)
- 65.94
- 131.88
- 197.82 (Correct answer)
- 263.76
Correct answer: 197.82
Volume = π × r² × h = 3.14 × 9 × 7 = 197.82 cubic units.
AMC 8 Geometry & Measurement 3
A square is inscribed in a circle of radius 5.
What is the area of the square?