Difference between revisions of "2021 AMC 12B Problems/Problem 15"
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==Video Solution by Interstigation==
==Video Solution by Interstigation ==
Revision as of 01:06, 9 June 2021
- The following problem is from both the 2021 AMC 10B #20 and 2021 AMC 12B #15, so both problems redirect to this page.
The figure is constructed from line segments, each of which has length . The area of pentagon can be written as , where and are positive integers. What is
Let be the midpoint of . Noting that and are triangles because of the equilateral triangles, . Also, and so .
Draw diagonals and to split the pentagon into three parts. We can compute the area for each triangle and sum them up at the end. For triangles and , they each have area . For triangle , we can see that and . Using Pythagorean Theorem, the altitude for this triangle is , so the area is . Adding each part up, we get .
Video Solution by OmegaLearn (Extending Lines, Angle Chasing, Trig Area)
Video Solution by Hawk Math
Video Solution by TheBeautyofMath
Video Solution by Interstigation (Ignore Useless Segments)
|2021 AMC 12B (Problems • Answer Key • Resources)|
|All AMC 12 Problems and Solutions|
|2021 AMC 10B (Problems • Answer Key • Resources)|
|All AMC 10 Problems and Solutions|