Relationship between junction area and voltage in forward biasing
Theoretically, p-n junction area has no influence on forward biasing voltage, as forward biasing voltage is a consequence of opposing an electric field normal to the contact surface between p region and n region (i.e. the vector representing the electric field has no component parallel to that surface).

Also, as you may suspect, p-n junction area influences the magnitude of the current running through.

Advice: find the appropriate book and work out the math leading to the Shockley diode equation to understand in detail the whole matter.