How do I find an area in m^2 when I'm given lengths in cm?

its tempting when we're given a length in cm - let's use a radius for example - to simply square the number of cm. However this can lead you into traps. Take a circle with radius 5cm. We know that A=pir^2. It is therefore tempting to say that the Area is pi25, getting 78.5 cm^2. So far, this is correct. The issue comes when we say that 78.5cm^2 is therefore 0.785m^2. But if we imagine our radius 5cm circle in one m^2, this obviously isn't right. To help avoid this, change the units to m before you do any calculation. 5cm=0.05m. So we do A=pi0.05^2 = pi0.0025 = 0.00785m^2. This, now, is the correct answer.