AMC12 Geometry 2 — Questions and Answers
Question 1: A triangle has vertices (0,0), (4,0), and (0,3). What is its area?
- 12
- 7
- 5
- 6 (Correct answer)
Correct answer: 6
Area=(1/2)*base*height=(1/2)(4)(3)=6.
Question 2: What is the sum of the interior angles of a hexagon?
- 540
- 1080
- 360
- 720 (Correct answer)
Correct answer: 720
The sum is (n-2)*180=(6-2)*180=720 degrees.
Question 3: A cylinder has radius 3 and height 4. What is its volume?
- 12pi
- 48pi
- 24pi
- 36pi (Correct answer)
Correct answer: 36pi
V=pi*r^2*h=pi(9)(4)=36pi.
Question 4: In a circle with radius 5, a chord is 8 units long. What is the distance from the center to the chord?
- 4
- 1
- 2
- 3 (Correct answer)
Correct answer: 3
Half the chord is 4; distance=sqrt(25-16)=3.
Question 5: Isosceles triangle ABC has AB=AC=10 and BC=12. What is its area?
- 60
- 36
- 24
- 48 (Correct answer)
Correct answer: 48
The altitude from A to BC is h=sqrt(100-36)=8; Area=(1/2)(12)(8)=48.
Question 6: The ratio of areas of two similar triangles is 4:9. What is the ratio of their perimeters?
- 4:9
- 8:27
- 16:81
- 2:3 (Correct answer)
Correct answer: 2:3
The ratio of lengths is sqrt(4/9)=2/3, so perimeters are in ratio 2:3.
AMC12 Geometry 2
A triangle has vertices (0,0), (4,0), and (0,3).
What is its area?