Difference between revisions of "2021 AMC 12B Problems/Problem 15"
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− | ==Problem | + | ==Problem 20== |
− | The | + | The figure is constructed from <math>11</math> line segments, each of which has length <math>2</math>. The area of pentagon <math>ABCDE</math> can be written is <math>\sqrt{m} + \sqrt{n}</math>, where <math>m</math> and <math>n</math> are positive integers. What is <math>m + n ?</math> |
+ | <asy> | ||
+ | /* Made by samrocksnature */ | ||
+ | pair A=(-2.4638,4.10658); | ||
+ | pair B=(-4,2.6567453480756127); | ||
+ | pair C=(-3.47132,0.6335248637894945); | ||
+ | pair D=(-1.464483379039766,0.6335248637894945); | ||
+ | pair E=(-0.956630463955801,2.6567453480756127); | ||
+ | pair F=(-2,2); | ||
+ | pair G=(-3,2); | ||
+ | draw(A--B--C--D--E--A); | ||
+ | draw(A--F--A--G); | ||
+ | draw(B--F--C); | ||
+ | draw(E--G--D); | ||
+ | label("A",A,N); | ||
+ | label("B",B,W); | ||
+ | label("C",C,W); | ||
+ | label("D",D,E); | ||
+ | label("E",E,dir(0)); | ||
+ | dot(A^^B^^C^^D^^E^^F^^G); | ||
+ | </asy> | ||
− | <math>\textbf{(A)} | + | <math>\textbf{(A)} ~20 \qquad\textbf{(B)} ~21 \qquad\textbf{(C)} ~22 \qquad\textbf{(D)} ~23 \qquad\textbf{(E)} ~24</math> |
Revision as of 19:48, 11 February 2021
Problem 20
The figure is constructed from line segments, each of which has length
. The area of pentagon
can be written is
, where
and
are positive integers. What is