1993 AHSME Problems/Problem 17
Problem
Amy painted a dartboard over a square clock face using the "hour positions" as boundaries.[See figure.] If is the area of one of the eight triangular regions such as that between 12 o'clock and 1 o'clock, and is the area of one of the four corner quadrilaterals such as that between 1 o'clock and 2 o'clock, then
Solution
Assume the length of the side of the square is 2, WLOG. This means the side of one t section is 1. As the lines are at clock face positions, each section has a degree angle from the center. So each section t is a triangle with a long leg of 1. Therefore, the short leg is .
This makes the area of each
The total area comprises , so
See also
1993 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 19 | |
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.