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2005 AMC 10A Question 20

AMC10 · 2005 AMC 10A

Question 20

An equiangular octagon has four sides of length $1$ and four sides of length $\dfrac{\sqrt{2}}{2},$ arranged so that no two consecutive sides have the same length. What is the area of the octagon?
  1. $\dfrac{7}{2}$
  2. $\dfrac{7\sqrt{2}}{2}$
  3. $\dfrac{5 + 4\sqrt{2}}{2}$
  4. $\dfrac{4 + 5\sqrt{2}}{2}$
  5. $7$