Problem
2021 AMC 10B Problem 20
The figure is constructed from 11 line segments, each of which has length 2. The area of pentagon ABCDE can be written as \sqrt{m} + \sqrt{n}, where m and n are positive integers. What is m + n ? ![[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,dir(0)); label("E",E,dir(0)); dot(A^^B^^C^^D^^E^^F^^G); [/asy]](/static/aops/ca5d16cb94b0f60a3c5c18f6c9766fed1c039219.png)
\textbf{(A)} ~20 \qquad\textbf{(B)} ~21 \qquad\textbf{(C)} ~22 \qquad\textbf{(D)} ~23 \qquad\textbf{(E)} ~24
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