Area of Triangles · Challenge problem

A tile is a $10$ cm by $10$ cm square. Four points are marked on its edges: $(3, 0)$, $(10, 3)$, $(7, 10)$ and $(0, 7)$, measuring in centimeters from the bottom-left corner. Joining them makes a tilted square inside the tile. What is the area of the tilted square, in square centimeters?