6 farms to 6 farms

Logic Level 4

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.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

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

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Didn't you use 11 sticks only? The middle two sticks didn't move.

Pi Han Goh - 5 years, 11 months ago

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No there are 12 sticks.How did you get 11?

A Former Brilliant Member - 5 years, 11 months ago

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Oh sorry. I can't count. You're right.

Pi Han Goh - 5 years, 11 months ago

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@Pi Han Goh – no problem.

A Former Brilliant Member - 5 years, 11 months ago

I did the exact same thing, but how can you show its the least area? Intuitively, I feel it's right, but how do you prove it?

Steven Mai - 5 years, 9 months ago

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