{"status": "success", "data": {"description_md": "Vertex $E$ of equilateral triangle $\\triangle ABE$ is in the interior of unit square $ABCD$. Let $R$ be the region consisting of all points inside $ABCD$ and outside $\\triangle ABE$ whose distance from $\\overline{AD}$ is between $\\frac{1}{3}$ and $\\frac{2}{3}$. What is the area of $R$?\n\n$\\textbf{(A)}\\ \\frac{12-5\\sqrt{3}}{72} \\qquad \\textbf{(B)}\\ \\frac{12-5\\sqrt{3}}{36} \\qquad \\textbf{(C)}\\ \\frac{\\sqrt{3}}{18} \\qquad \\textbf{(D)}\\ \\frac{3-\\sqrt{3}}{9} \\qquad \\textbf{(E)}\\ \\frac{\\sqrt{3}}{12}$\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": "

Vertex E of equilateral triangle \\triangle ABE is in the interior of unit square ABCD. Let R be the region consisting of all points inside ABCD and outside \\triangle ABE whose distance from \\overline{AD} is between \\frac{1}{3} and \\frac{2}{3}. What is the area of R?

\\textbf{(A)}\\ \\frac{12-5\\sqrt{3}}{72} \\qquad \\textbf{(B)}\\ \\frac{12-5\\sqrt{3}}{36} \\qquad \\textbf{(C)}\\ \\frac{\\sqrt{3}}{18} \\qquad \\textbf{(D)}\\ \\frac{3-\\sqrt{3}}{9} \\qquad \\textbf{(E)}\\ \\frac{\\sqrt{3}}{12}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2008 AMC 12B Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc12B_p14", "prev": "/problem/08_amc12B_p12"}}