# 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