The correct answer is: C. Increases with depth of the wall.
The pressure exerted by water on a dam is equal to the weight of the water above it. The deeper the water, the more water there is above it, and the greater the pressure. This is why the wall of a dam is made thicker at the bottom than at the top. The thicker wall at the bottom can withstand the greater pressure of the water.
Option A is incorrect because the pressure exerted by water on a dam does not depend on the thickness of the wall. The pressure is only dependent on the depth of the water.
Option B is incorrect because the pressure exerted by water on a dam increases with depth, not height. The higher the wall, the greater the pressure, but the pressure is not directly proportional to the height of the wall.
Option D is incorrect because the pressure exerted by water on a dam does not depend on the area of the wall. The area of the wall only affects the amount of water that is held back by the dam, not the pressure of the water.