{"status": "success", "data": {"description_md": "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 $m + n ?$\n\n<center>\n<img class=\"problem-image\" height=\"252\" src=\"https://latex.artofproblemsolving.com/8/d/3/8d30b5bdb8799955b16c29f895eab1b33ec5d028.png\" width=\"225\"/>\n</center>\n\n$\\textbf{(A)} ~20 \\qquad\\textbf{(B)} ~21 \\qquad\\textbf{(C)} ~22 \\qquad\\textbf{(D)} ~23 \\qquad\\textbf{(E)} ~24$", "description_html": "<p>The figure is constructed from  <span class=\"katex--inline\">11</span>  line segments, each of which has length  <span class=\"katex--inline\">2</span> . The area of pentagon  <span class=\"katex--inline\">ABCDE</span>  can be written as  <span class=\"katex--inline\">\\sqrt{m} + \\sqrt{n}</span> , where  <span class=\"katex--inline\">m</span>  and  <span class=\"katex--inline\">n</span>  are positive integers. What is  <span class=\"katex--inline\">m + n ?</span> </p>\n<center>\n<img class=\"problem-image\" height=\"252\" src=\"https://latex.artofproblemsolving.com/8/d/3/8d30b5bdb8799955b16c29f895eab1b33ec5d028.png\" width=\"225\"/>\n</center>\n<p> <span class=\"katex--inline\">\\textbf{(A)} ~20 \\qquad\\textbf{(B)} ~21 \\qquad\\textbf{(C)} ~22 \\qquad\\textbf{(D)} ~23 \\qquad\\textbf{(E)} ~24</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2021 AMC 10B Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc10B_p21", "prev": "/problem/21_amc10B_p19"}}