2021 Fall AMC 12A Problems/Problem 21
Problem
Let be an isosceles trapezoid with and . Points and lie on diagonal with between and , as shown in the figure. Suppose , , , and . What is the area of
Solution
First realize that Thus, because we can say that and From the Pythagorean Theorem, we have and Because from the problem statement, we have that Solving, gives To find the area of the trapezoid, we can compute the area of and add it to the area of Thus the area of the trapezoid is Thus the answer is
~NH14
See Also
2021 Fall AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 20 |
Followed by Problem 22 |
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 12 Problems and Solutions |