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2007 AMC 10B Question 23

AMC10 · 2007 AMC 10B

Question 23

A pyramid with a square base is cut by a plane that is parallel to its base and is $2$ units from the base. The surface area of the smaller pyramid that is cut from the top is half the surface area of the original pyramid. What is the altitude of the original pyramid?
  1. $2$
  2. $2+\sqrt2$
  3. $1+2\sqrt2$
  4. $4$
  5. $4+2\sqrt2$