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geometry intermediate

Problem

Regular hexagon is divided into six smaller equilateral triangles, such as , shown in boldface in the diagram. By connecting every other vertex, we obtain a larger equilateral triangle , also shown in boldface. Compute the ratio .
problem
Solution
Each small congruent right triangle in the diagram has the same area, which we will call . Since consists of two small triangles, . Similarly, is built from six small triangles, so . Hence the ratio of these areas is .
Final answer
\frac{1}{3}