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# The Farmers' Field Boundary

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Age 11 to 14

Challenge Level

*The Farmers' Field Boundary printable sheet*

Two farmers each have a field with a shared boundary. On the boundary is a tap.

The farmers decide it would be more convenient if the boundary was a straight line, but they both need to access the tap.

Your challenge is to redraw the boundary so that:

- Both farmers can access the tap
- The boundary line is straight
- The new fields have the same areas as the original fields

You can use the interactivity below to explore this problem with a variety of fields.

Move the points to create two fields, then click Fix Fields.

Once you have created your fields, a purple dot will appear which you can move to create the new field boundary.

**When you think your new fields have the same area as the original fields, you can tick the "Show areas" box to see how close you are.**

**Can you come up with a geometrical method for constructing the position of the new boundary?**

Can you adapt your method to construct a boundary for a more complicated situation like the one pictured below?

Can you describe a method for redrawing boundaries with four, five, or more straight lines into a single straight line?