The force exerted on the same amount of area is not less on top of a mountain than at sea level. In fact, the force exerted by air pressure is greater at higher elevations. This is because the weight of the air above a given point increases as you move higher in the atmosphere.

At sea level, the air pressure is about 14.7 pounds per square inch (psi). This means that every square inch of surface area at sea level is experiencing a force of 14.7 pounds. As you move up in elevation, the air pressure decreases, but the force exerted on a given area remains the same. This is because the weight of the air above a given point is distributed over a larger area as you move higher.

For example, at the top of Mount Everest, the air pressure is only about 0.33 psi. However, the force exerted on a given area at the top of Mount Everest is still the same as at sea level, which is 14.7 pounds per square inch. This is because the weight of the air above a given point at the top of Mount Everest is distributed over a much larger area than at sea level.