{"status": "success", "data": {"description_md": "Let $ABCDEF$ be a regular hexagon with side length $1$. Denote by $X$, $Y$, and $Z$ the midpoints of sides $\\overline {AB}$, $\\overline{CD}$, and $\\overline{EF}$, respectively. What is the area of the convex hexagon whose interior is the intersection of the interiors of $\\triangle ACE$ and $\\triangle XYZ$?\n\n$\\textbf{(A)}\\ \\frac {3}{8}\\sqrt{3} \\qquad \\textbf{(B)}\\ \\frac {7}{16}\\sqrt{3} \\qquad \\textbf{(C)}\\ \\frac {15}{32}\\sqrt{3} \\qquad  \\textbf{(D)}\\ \\frac {1}{2}\\sqrt{3} \\qquad \\textbf{(E)}\\ \\frac {9}{16}\\sqrt{3}$", "description_html": "<p>Let  <span class=\"katex--inline\">ABCDEF</span>  be a regular hexagon with side length  <span class=\"katex--inline\">1</span> . Denote by  <span class=\"katex--inline\">X</span> ,  <span class=\"katex--inline\">Y</span> , and  <span class=\"katex--inline\">Z</span>  the midpoints of sides  <span class=\"katex--inline\">\\overline {AB}</span> ,  <span class=\"katex--inline\">\\overline{CD}</span> , and  <span class=\"katex--inline\">\\overline{EF}</span> , respectively. What is the area of the convex hexagon whose interior is the intersection of the interiors of  <span class=\"katex--inline\">\\triangle ACE</span>  and  <span class=\"katex--inline\">\\triangle XYZ</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac {3}{8}\\sqrt{3} \\qquad \\textbf{(B)}\\ \\frac {7}{16}\\sqrt{3} \\qquad \\textbf{(C)}\\ \\frac {15}{32}\\sqrt{3} \\qquad  \\textbf{(D)}\\ \\frac {1}{2}\\sqrt{3} \\qquad \\textbf{(E)}\\ \\frac {9}{16}\\sqrt{3}</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": 4, "problem_name": "2018 AMC 10B Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc10B_p25", "prev": "/problem/18_amc10B_p23"}}