2012 AMC 10B Problems/Problem 14
Solution
Observe that the rhombus is made up of two congruent equilateral triangles with side length equal to GF. Since AE has length and triangle AEF is a 30-60-90 triangle, it follows that EF has length 1. By symmetry, HG also has length 1. Thus GF has length . The formula for the area of an equilateral triangle of length s is . It follows that the area of the rhombus is:
Thus, answer choice D is correct.