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As this question was originally placed in Australian football categories, it has been answered from that reference, as the same grounds are used for both - cricket and football - at different seasons of the year:

Firstly, there are no set dimensions for cricket or football grounds; most grounds can be anywhere from 137 to 180 metres in length and about 25 or 30 metres less in width. The minima laid down by cricket authorities are that length must be at least 137 metres and width at least 65 yards, but widths in real cricket pitches are never anything close to being so small.

So, if we take a ground of [say] 165 X 135 metres, you could virtually average those two figures and apply your mathematical formula for calculating the area of a circle => Area = pi X r X r, and, although not a 100% accurate method of calculating the area of an oval, the answer, via this method, would come mighty close, as the grounds are only mildly eliptical. And as grounds vary quite extensively, the answer would certainly be correct for many grounds in Australia:

The approx answer to the calculation is 70700 sq metres.

The reality is, however, that some grounds are larger, others smaller.

It is an oval field and has a 66ft.(20m.) strip of ground in the middle of the field.

Please Note: The same grounds are used for one day cricket and for T20 cricket - without size modification.

Q: What are the dimensions of a cricket field in square meters?

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