Shown here is a farm, subdivided into 6 smaller camps using 13 sticks. If the length of a matchstick is 1 unit, the total area of the farm is 3 square units.

Rearrange the sticks, using only 12 sticks, to form another farm, again with 6 camps. All sticks must be flat on the surface and no sticks may be broken. Find the least area of the farm in square units to three decimal places. You may use a calculator.

The answer is 2.598.

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Applying Pythagoras theorem: (0.5)² + (A)² = (r)² (where r=1) A²= (0.75)² A = 0.866 units

The total area of the 6 triangles: = 6 X (1/2 X 1 X 0.866) = 6 X 0.433 = 2.598 square units