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Shown here is a farm, subdivided into 6 smaller camps using 13 matchsticks. If the length of a matchstick is 1 unit, the total area of the farm is 3 square units.
Can you rearrange the matchsticks, using ONLY 12, to form another farm, again with 6 camps, so that the total area of the farm is between 2.5 and 3 square units? All matchsticks must be flat on the surface and no matchsticks may be broken.
Applying Pythagoras:
(0.5)² X (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
(0.5)² X (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
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