{"status": "success", "data": {"description_md": "Regular octagon $ABCDEFGH$ has area $n$. Let $m$ be the area of quadrilateral $ACEG$. What is $\\tfrac{m}{n}?$\n\n$\\textbf{(A) } \\frac{\\sqrt{2}}{4} \\qquad \\textbf{(B) } \\frac{\\sqrt{2}}{2} \\qquad \\textbf{(C) } \\frac{3}{4} \\qquad \\textbf{(D) } \\frac{3\\sqrt{2}}{5} \\qquad \\textbf{(E) } \\frac{2\\sqrt{2}}{3}$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Regular octagon  <span class=\"katex--inline\">ABCDEFGH</span>  has area  <span class=\"katex--inline\">n</span> . Let  <span class=\"katex--inline\">m</span>  be the area of quadrilateral  <span class=\"katex--inline\">ACEG</span> . What is  <span class=\"katex--inline\">\\tfrac{m}{n}?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } \\frac{\\sqrt{2}}{4} \\qquad \\textbf{(B) } \\frac{\\sqrt{2}}{2} \\qquad \\textbf{(C) } \\frac{3}{4} \\qquad \\textbf{(D) } \\frac{3\\sqrt{2}}{5} \\qquad \\textbf{(E) } \\frac{2\\sqrt{2}}{3}</span> </p>&#10;<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": "2020 AMC 12A Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc12A_p15", "prev": "/problem/20_amc12A_p13"}}