Difference between revisions of "1985 AHSME Problems/Problem 13"
(Created page with "==Problem== Pegs are put in a board <math> 1 </math> unit apart both horizontally and vertically. A rubber band is stretched over <math> 4 </math> pegs as shown in the figure, fo...") |
|||
Line 38: | Line 38: | ||
==See Also== | ==See Also== | ||
{{AHSME box|year=1985|num-b=12|num-a=14}} | {{AHSME box|year=1985|num-b=12|num-a=14}} | ||
+ | {{MAA Notice}} |
Revision as of 12:00, 5 July 2013
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
Solution 1
We see that the number of interior points is and the number of boundary points is . Therefore, by Pick's Theorem, the area is .
Solution 2
Draw in the perimeter of the rectangle and label the points as shown. We have , , , , and . Therefore, .
See Also
1985 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.