Question

A grassy plot is 100× 80m . Two cross path of 5m width are constructed at right angle through the centre of field and parallel to the sides of plot . Find the total area as path

Answer 1

Given
length of plot=100m
breadth of plot=80m
width of path=5m

area of path ABCD = L x B
L=100m
B=5m
therefore area
=100x5m
=500m

area of path EFGH = L x B
L=5m
B=80m
therefore area
=5x80m
=400m

area of path where intersection takes place
i.e., cross roads (IJKL)
area of IJKL = L x B
L=5m
B=5m
therefore area
=5x5
=25m

total area of path= ar(ABCD) + ar(EFGH) - ar(IJKL)
=500+400-25
=875m

NOTE AREA OF IJKL IS SUBSTRACTED BECAUSE AREA OF IJKL WAS INCLUDED TWICE IN CALCULATION OF BOTH PATHS i.e., IT WAS INCLUDED IN CALCULATION OF AREA OF PATH ABCD AND ALSO IN CALCULATION OF AREA OF EFGH. SO AREA OF IT IS CALCULATED AND DEDUCTED ONCE.