Scale Diagrams and Building Model Calculations

A building has a perimeter of \(8\) cm, with a gate of width \(0.5\) cm on a map. If the actual perimeter of the building is \(0.56\) km,

1. find the scale of the map in the form \(1:r\).
2. A model of the building is made to another scale of \(1:5000\).
   Calculate
   1. the width of the gate in centimetres as represented by the second scale.
   2. the floor area of the building model in square centimetres if the actual floor area of the building is \(16000\) m\(^{2}\).