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why does area equals pi times the radius squared calculate the area of a circle after all this seems like a magic formula but how do you know you can trust it you already know that area equals pi r squared is the formula to calculate the area of a circle now heres a sloppy proof to explain it if you multiply the radius squared you get the area of this square a here now combine 4 of square a and you have this larger square b circumscribed around your original circle now thats too large of an area because we dont want to include these corners so we need to multiply by a value less than 4. hey look 3.14 works perfectly but you know this seems arbitrary like a really lucky guess theres no clear justification for why we should use pi we need a better way to prove that what were doing is correct in this lesson you will learn how to prove the area of a circle by dissecting and rearranging the circle lets review two concepts youre already familiar with first circumference is the distan