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The force does take into account area. Remember, Force = Pressure x Area. Imagine a brick on its long flat side. The pressure is much smaller on that side, distributed over a large area. Now turn the brick on one of its smaller sides. The pressure is much larger on that side, but distributed over a smaller area. Overall, however, the frictional force is the same, since the table exerts the same normal force on the brick.
 
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