A Christmas Present

Topic: Plane Geometry
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A group of friends decide to send their math teacher a gift for Christmas. They want this gift to be a surprise, so they decide to hide it behind the tree. How big is the biggest possible square gift, and how much room is left over if the tree has sides of 13 cm and a base of 10 cm?

Common Core Standards: 7.G.6
Problem #: 
238 (2011-2012)
Problem Difficulty Level: 6 [?]