2024 AMC 10A Problems/Problem 22
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
?
03abbd4df2932f4a1d16a34c2b9e15b683dedb.png
Solution
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
.
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 |
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.