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)
The area is
Therefore, the answer is .
~Steven Chen (www.professorchenedu.com)
Solution 3
We start by finding the points. The outlined shape is made up of . By the Shoelace Theorem, we find the area to be , or .
https://artofproblemsolving.com/wiki/index.php/Shoelace_Theorem
~Taco12
~I-AM-DA-KING for the link
Solution 4
We can use Pick's Theorem. We have interior points and boundary points. By Pick's Theorem, we get Checking our answer choices, we find our answer to be .
~danprathab
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.