Problem:
The horizontal and vertical distances between adjacent points equal unit. The area of triangle is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
From the total area of , subtract the areas of the four surrounding polygons whose areas are indicated in the diagram. Thus the area of the remaining triangle is
Note. Points whose coordinates are integers are called lattice points. According to Pick's Theorem, if there are lattice points in the interior of a triangle and lattice points on the boundary, then the area of the triangle is . In this problem, and . Therefore the area of the triangle is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions