AMC12 Geometry

Question 1

A circle has area 16pi. What is its circumference?

Accepted Answer

8pi

Answer

From pi*r^2=16pi we get r=4, so C=2pi(4)=8pi.

Question 2

In right triangle ABC with right angle at B, AB=5 and BC=12. What is sin(A)?

Accepted Answer

12/13

Answer

The hypotenuse AC=13, and sin(A)=BC/AC=12/13.

Question 3

The diagonals of a rhombus are 6 and 8. What is its side length?

Accepted Answer

5

Answer

The half-diagonals are 3 and 4; side=sqrt(9+16)=5.

Question 4

A rectangle has perimeter 34 and area 60. What is the length of its diagonal?

Accepted Answer

13

Answer

l+w=17 and lw=60 gives l=12,w=5; diagonal=sqrt(144+25)=13.

Question 5

What is the area of an equilateral triangle with side length 4?

Accepted Answer

4sqrt(3)

Answer

Area=(sqrt(3)/4)*s^2=(sqrt(3)/4)*16=4sqrt(3).

AMC12 - American Mathematics Competition 12 Practice Test