Let ABCD be the rectangular field with length AB = 100m and breadth BC = 90m
In fig, two paths each of the width 2.5m parallel to the breadth are shown in orange color and two paths each of width 2m parallel to the length are shown in yellow color.
Now, area of orange colored paths = 2 x (2.5 x 90) = 450 m^2
Area of yellow colored paths = 2 x (2 x 100) = 400 m^2
It can be seen that the red colored paths are overlapping four times, so we need to remove it while calculating total area of the path
(1) Total area of path = (area of orange colored paths) + (area of yellow colored paths) – (area of red colored paths)
= (450) + (400) – ( 4 x (2.5 x 2) )
= 450 + 400 – 20
= 830 m^2
Hence, total area of the path is 830 m^2
(2) Total area of rectangular field = 100m x 90m = 9000 m^2
So, area of remaining portion of rectangular field = (total area of rectangular field) – (total area of the path)
= 9000 – 830
= 8170 m^2
Hence, area of the remaining portion of the rectangular field is 8170 m^2