the solution to this math riddle?

Ermee

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i had someone teach me some math and they gave me a riddle where we found out the area of a square. then he took the square apart and made it into a triangle. we then figured out the area of that triangle and it was one more than the area of the original square. he told me to figure out how that happened. i think it was something where he changed the shape of the square into the triangle but im not sure. can anyone explain this to me?
 
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