The layout used is shown above. Since the answer doesn’t depend on shape of the rectangular field, we can derive the answer by considering it to be a square. All triangles are similar with non-hypotenuse side ratios of 2:1. Using BC as a unit of length, triangles ABC and ADE are similar with ADE being double the size of ABC. So the side CE of the central square field is 2 and the whole field has a side length AD of \(2\sqrt{5}\). Hence AD/BC = \(1/\sqrt{5}\), which means that the area ratio of the inner and outer squares is \(1/5\) making the central field 11 hectares. The red figures show the relative areas of all the sub-fields.

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