I was completely baffled by this problem today and still don't understand it. I'm trying to figure out if (the area of a square with sides of 1cm) or (10mm) is larger. I decided to figure the area of the square first (1cm x 1cm = 1cm). Simple. Then I know 10mm=1cm, so I concluded the two options are equal. Yet, if I covert the cm to mm first, I have to figure the area of a square with the sides of 10mm. (10mm x 10mm = 100mm) 100mm is certainly greater than 10mm, so now the first option appears to be larger. I am very confused. Why does it matter if I convert first or second? Did I somehow manage to majorly mess up a basic math question? Any insights?
Converting Units and Finding Area
- Thread starter GREtaker
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mmm4444bot
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The units for area are always squared units.
100 square millimeters equals 1 square centimeter.
Any two squares having the same side length must have the same area. :cool:
It makes no difference which way you convert.
Square with a side of 1 cm. But that means that the square also has a side of 10 mm.
So one way to compute the area of the square is 1 centimeter * 1 centimeter = 1 centimeter squared = 1 square centimeter.
Another way 10 millimeters * 10 millimeters = 100 millimeters squared = 100 square millimeters.
Because it is the same square, it must have the same area.
Congratulations. You have just demonstrated that 1 square centimeter equals 100 square millimeters.