A room 8.5m long and 4.5m wide is surrounded by a balcony 2m wide. Find the area occupied by the balcony

Since your balcony is 2m wide, length of the balcony would be

8.5m+2m+2m = 12.5m

similarly you can calculate the other dimension

4.5m+2m+2m = 8.5m

now,

area_of_balcony_and_room = area_of_balcony + area_of_room

or,

area_of_balcony = area_of_balcony_and_room - area_of_room

therefore,

area_of_balcony = 12.5*8.5 - 8.5*4.5 = 68sqm