The medieval soldier would have been much practiced at hand to hand combat, he would have known where exactly to place his sword, as seen in the sculpture, for maximum effect. These vulnerable areas were the groin, armpit and the throat, a place uncovered for flexibility
The halberd and the poleaxe were also popular, by the fifteenth century the broad axe, a weapon a bit like the Viking axe, were being used too.
All these weapons could be used in a different way against plate armour, to cut through, punch through, or crush the poor medieval soldier.
The lance, as seen here being used by the mounted soldier, were not exactly like the lances used in jousting, they were more like spears, they were long and made to be used with one hand, and of course the ends were sharpened to a point.
Interesting, and I learnt this yesterday, a lance also refers to a unit of soldiers, who would surround a nobleman as he went into battle. The Lance was usually made up of squires, other mounted soldiers and of course the knight himself.
Here's another photograph I took yesterday when we visited the Richard III Visitor Centre in Leicester.