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Pressure as force over area

Pressure ($$P$$ or $$p$$) is the magnitude of the force exerted on an object per unit area of the object's surface: $$$\Torange{\text{Pressure}} = \Torange{P} =\dfrac{\Tblue{\text{Force}}}{\Tred{\text{Area}}} = \dfrac{\Tblue{F}}{\Tred{A}} $$$

When walking on top of fresh snow in normal shoes, you sink through the snow's surface. Your shoes have a low surface area so the pressure on the surface of the snow is high.

Skis have a greater surface area than normal shoes and so the pressure you apply to the surface of the snow is lower. This allows you to stay on the surface without sinking in.

The walker sinks into the snow while the skier is able to stay on the surface.
The walker sinks into the snow while the skier is able to stay on the surface.

Pressure is a scalar, not a vector quantity. In other words, it has no direction.