1985 AHSME Problems/Problem 13
Contents
[hide]Problem
Pegs are put in a board unit apart both horizontally and vertically. A rubber band is stretched over pegs as shown in the figure, forming a quadrilateral. Its area in square units is
Solution 1
We draw in the rectangle bounding the given quadrilateral and label the points as shown. The area of rectangle is , while the areas of the triangles , , , and are, respectively, Hence the area of the given quadrilateral is .
Solution 2
The number of lattice points (i.e. pegs on the board) strictly inside the quadrilateral is and the number of lattice points on its boundary is . Therefore, by Pick's theorem, its area is .
See Also
1985 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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