2021 Fall AMC 12B Problems/Problem 2
- The following problem is from both the 2021 Fall AMC 10B #2 and 2021 Fall AMC 12B #2, so both problems redirect to this page.
Contents
Problem
What is the area of the shaded figure shown below?
Solution 1 (Area Addition)
The line of symmetry divides the shaded figure into two congruent triangles, each with base and height
Therefore, the area of the shaded figure is ~MRENTHUSIASM ~Wilhelm Z
Solution 2 (Area Subtraction)
To find the area of the shaded figure, we subtract the area of the smaller triangle (base and height ) from the area of the larger triangle (base and height ): ~MRENTHUSIASM ~Steven Chen (www.professorchenedu.com)
Solution 3 (Shoelace Theorem)
The consecutive vertices of the shaded figure are and By the Shoelace Theorem, the area is ~Taco12 ~I-AM-DA-KING
Solution 4 (Pick's Theorem)
We have lattice points in the interior and lattice points on the boundary. By Pick's Theorem, the area of the shaded figure is ~danprathab
Video Solution by Interstigation
https://youtu.be/p9_RH4s-kBA?t=110
~Interstigation
Video Solution
~Education, the Study of Everything
Video Solution by WhyMath
~savannahsolver
Video Solution by TheBeautyofMath
For AMC 10: https://youtu.be/lC7naDZ1Eu4?t=512
For AMC 12: https://youtu.be/yaE5aAmeesc?t=512
~IceMatrix
See Also
2021 Fall AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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 |
2021 Fall AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 1 |
Followed by Problem 3 |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.