Problem 5 · 2013 Math Kangaroo
Easy
Geometry & Measurement
areagridspatial-reasoning
On a square grid made up of unit squares, six points are marked as shown. Three of them form a triangle with the least area. How big is this smallest area?
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Answer: A — \(\frac{1}{2}\)
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Hint 1 of 2
The smallest possible triangle area on a unit grid is very small — look for three points that are nearly in a line.
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Hint 2 of 2
A triangle with base 1 and height 1 already has area 1/2; check whether any triple beats that, or whether 1/2 is the minimum here.
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Approach: find the three marked points giving the least area
- On a unit grid, the smallest triangle from lattice points has area 1/2 (base 1, height 1).
- Among the six marked points, a triple forms exactly such a minimal triangle.
- So the smallest area is 1/2.
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