The pond and the path have a combined radius of 6 meters (the radius of the pond plus the width of the path). Then, find the combined area of the path and the pond by using the formula for the area of a circle . The formula works out to 36.

Now the area of the smaller circle (with radius of 5m) needs to be deducted from the area of the larger circle (with radius of 6m).

`36 pi - 25 pi = 11 pi`  

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This renders an answer of 34.56`m^2`  rounded to 2 decimal places and as the question asks for 3 significant figures this needs to be rounded off to 34.6 `m^2`  

Ans: The area of the path is  34.6`m^2` rounded off to three significant figures.