Help with pressure-force problem

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To calculate the force exerted on the car door by the water, the total pressure at a depth of 13.7 m must be considered, which includes atmospheric pressure and the pressure due to the water column. The formula used is Force = pressure * area, where pressure is the sum of atmospheric pressure and the hydrostatic pressure calculated using the water density and depth. The user initially calculated the force as 351582 N but suspects an error in their approach. They contemplate whether the car's air might affect the pressure calculation but are reminded that atmospheric pressure should not be neglected. Clarification on the correct application of pressure calculations is needed to resolve the discrepancy.
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Homework Statement



A car misses a turn, sinks into a shallow lake, coming to rest on its side with the door horizontal and at a depth of 13.7 m. If the area of the car door is 0.67 m^{2}, what is the force exerted on the outside of the door by the water?

Homework Equations



Force = pressure * area

The Attempt at a Solution



p_total = p_atm + \rho * g * h

F = (p_atm + \rho * g * h)/area

F = (101325 N/m^{2} + (1000 kg/m^{3} * 9.8 m/s^{2} * 13.7 m)) / .67 m^{2} = 351582 N

That's what I've done so far, but it isn't the right answer, can someone help point me in the right direction? I know I did something wrong or forgot something but don't know what it is. Thanks in advance!
 
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Maybe the car is still filled with air so that the atmospheric pressure cancels out (it takes some time to fill with water anyway even if the windows are open).
 
No, it tells me to not forget to add the atmospheric pressure.
 

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