Area of Path and Verandah

Area of Path & Verandah: 

 It is observed that in square or rectangular gardens or parks. Some space in the form of path is left inside or outside or in between as cross paths.

Illustration: A footpath of uniform width 5 m runs round the inside of a rectangular park 38 m long and 32 m wide. Find the area of the path.

Solution: Let ABCD be the rectangular park and PQRS be the internal boundaries of the path.

We have, Length AB= 38 m and Breadth BC= 32 m:

Thus, Area of rectangle ABCD = AB  BC = 38 m  32 m = 1216 

Now, Length PQ  = 38 m - 5 m - 5 m = 28 m and Breadth QR = 32 m - 5 m - 5 m = 22m

Area of rectangle PQRS = PQ  RS = 28 m  22 m = 616 

Area of footpath = Area of rectangle ABCD - Area of rectangle PQRS = 1216 - 616=600 

Thus, Area of footpath =600 

The area of the crossroads = Area of the two colored rectangles - Area of the red colored rectangle at the centre.

We are subtracting the area of the rectangle because we are taking it into consideration two times.

Illustration: A rectangular lawn is 30 m by 20 m .It has two roads each 2 m wide running in the middle of it, one parallel to the length and the other parallel to the breadth . Find the area of the roads.

Solution: Let EFGH and PQRS be the cross roads,

we have EH = 2 m and EF = 30 m, then

Area of path EFGH =  EH EF = 2 m    30 m  = 60 

Now, for the other crossroad, PQ = 2 m and QR = 20 m,

then Area of path  PQRS = PQ   QR = 2 m    20 m = 40 

Area KLMN is common to the both the paths: KL = 2 m and LM = 2 m, then Area of KLMN  =  KL LM = 2 m   2 m = 4 

Total area covered  as roads = Area of road EFGH + Area of road PQRS - Area of  KLMN = 60 + 40 - 4 =  100 - 4  = 96 

Thus, total area of the roads = 96