A metal plate with a circular hole at the centre is heated. What will happen to the area of the hole ?

Assuming the disc is uniform and isotropic (the same in different directions), the hole will expand in the same ratio as the metal. It is because the thermal expansion equation applies to all lengths associated with the metal, including the circumference of the hole, since the edge of the hole is made out of metal. And if the circumference of the hole expands, so does the diameter.