Problem 9 · 2020 Math Kangaroo
Stretch
Geometry & Measurement
areagrid
Four points were marked on a grid of 1 cm side squares. Of the possible triangular regions that can be obtained with vertices at three of these points, one has the largest area. What is this area, in cm²?
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Answer: D — 5.5
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Hint 1 of 2
List the four marked lattice points, then think which three are spread out most.
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Hint 2 of 2
Use the shoelace formula (or base×height) on the most spread-out triple.
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Approach: compute triangle areas on the lattice and take the largest
- The points are at (2,4), (5,2), (1,1) and (2,1) on the cm grid.
- The triangle (2,4), (5,2), (1,1) has area ½|2(2−1)+5(1−4)+1(4−2)| = ½·11 = 5.5.
- The other triples give smaller areas (4.5, 1.5, 0.5).
- So the largest area is 5.5 cm².
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