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2007 AMC 12B Question 25

AMC12 · 2007 AMC 12B

Question 25

Points $A,$ $B,$ $C,$ $D,$ and $E$ are located in $3$-dimensional space with $AB=BC=CD$ $=DE=EA=2$ and $\angle ABC=\angle CDE$ $=\angle DEA=90^\circ.$ The plane of $\triangle ABC$ is parallel to $\overline{DE}.$ What is the area of $\triangle BDE?$
  1. $\sqrt{2}$
  2. $\sqrt{3}$
  3. $2$
  4. $\sqrt{5}$
  5. $\sqrt{6}$