Difference between revisions of "1998 AJHSME Problems/Problem 6"
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* [[AJHSME Problems and Solutions]] | * [[AJHSME Problems and Solutions]] | ||
* [[Mathematics competition resources]] | * [[Mathematics competition resources]] |
Revision as of 23:03, 9 June 2011
Contents
[hide]Problem 6
Dots are spaced one unit apart, horizontally and vertically. The number of square units enclosed by the polygon is
Solution 1
By inspection, you can notice that the triangle on the top row matches the hole in the bottom row.
This creates a box, which has area
Solution 2
We could take the area of each square.
Top-left: Top: Triangle with area Top-right: Left: Square with area Center: Square with area Right: Square with area Bottom-left: Square with area Bottom: Triangle with area Bottom-right: Square with area
Adding all of these together, we get or
See also
1998 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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 | ||
All AJHSME/AMC 8 Problems and Solutions |