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1973 AMC 12 Question 4

AMC12 · 1973 AMC 12

Question 4

Two congruent $30^\circ$-$60^\circ$-$90^\circ$ triangles are placed so that they overlap partly and their hypotenuses coincide. If the hypotenuse of each triangle is $12,$ the area common to both triangles is
  1. $6\sqrt3$
  2. $8\sqrt3$
  3. $9\sqrt3$
  4. $12\sqrt3$
  5. $24$