Difference between revisions of "2024 AMC 10A Problems/Problem 22"
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==Solution 2== (WIP) | ==Solution 2== (WIP) | ||
| − | ~YTH (Working on it right now, please don't interfere. Thanks :)) | + | ~YTH (Working on it right now, please don't interfere. Thanks :) also if someone could help me create the solution 2 header that would be awesome) |
Revision as of 18:37, 8 November 2024
Problem
Let 
be the kite formed by joining two right triangles with legs 
and 
along a common hypotenuse. Eight copies of are used to form the polygon shown below. What is the area of triangle 
?
Solution 1
Let be quadrilateral MNOP. Drawing line MO splits the triangle into 
.
Drawing the altitude from N to point Q on line MO, we know NQ is 
, MQ is 
, and QO is 
.
Due to the many similarities present, we can find that AB is 
, and the height of is 
AB is 
and the height of is 
.
Solving for the area of gives 
which is 
~9897 (latex beginner here)
==Solution 2== (WIP)
~YTH (Working on it right now, please don't interfere. Thanks :) also if someone could help me create the solution 2 header that would be awesome)
See also
| 2024 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 21 |
Followed by Problem 23 | |
| 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 AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
