Check the ionic charges of the metals. What do you see? They all have + charges in ion form. This means, they tend to lose electrons, which, in turn, means that they have electrons so far from the nucleus that it's preferable to lose some rather than gain some. read more
Metal atoms become cations by releasing electrons. This means that it must have electrons in larger number than the cation. Hence the electrons will occupy larger number of valence shells. Hence it has a larger size. On the other hand, nonmetal atoms form anions by gaining electrons. Hence it has a lesser number of electrons than anion. read more
Non-metal ions typically form negative ions (ie: Cl-) Therefore they now have an extra electron which is protected from the positive pull of the nucleus by the other electrons and therefore the electron shell has now expanded, making nonmetal ions larger than nonmetal atoms. read more
A nonmetal atom will do it opposite. It NEEDS and electron to look like the Noble Gas that comes AFTER it on the periodic table (this is known as the Octet Rule, btw). Therefore, it will GAIN an electron, to become a larger nonmetal ion known as an anion because it is negatively charged. read more