Problem:
Which of the following polygons has the largest area?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Areas may be found by dividing each polygon into triangles and squares as shown.
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Note: Pick's Theorem may be used to find areas of geoboard polygons. If is the number of dots inside the figure, is the number of dots on the boundary and is the area, then . Geoboard figures in this problem have no interior points, so the formula simplifies to . For example, in polygon the number of boundary points is and .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions