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In order to answer that, you would need to know the configuration of the path,

that is, where it goes. Does it provide a route down the center of the lawn's length ?

Does it cut across the lawn's breadth ? Does it connect one corner of the lawn

diagonally to the opposite corner ?

Perhaps the path is immediately adjacent to the outline of the lawn, and takes you

completely around it. In that case, the path is simply a long rectangle that has been

bent into four straight segments and laid along the lawn's outer edge. If the rectangle

were reassembled by laying the four segments straight in line again, it would be

2m wide, and equal in length to the distance around the lawn (the perimeter).

Surely you would have no trouble calculating the area of that long narrow rectangle,

if that were the path's configuration.

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Q: How do you find the area of path if the lawn is 34m long 24m broad and the path 2m wide?
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