{"status": "success", "data": {"description_md": "A unit square is rotated $45^\\circ$ about its center.  What is the area of the region swept out by the interior of the square?\n\n$\\textbf{(A)}\\ 1 - \\frac{\\sqrt2}{2} + \\frac{\\pi}{4}\\qquad\\textbf{(B)}\\ \\frac{1}{2} + \\frac{\\pi}{4} \\qquad\\textbf{(C)}\\ 2 - \\sqrt2 + \\frac{\\pi}{4}$\n$\\textbf{(D)}\\ \\frac{\\sqrt2}{2} + \\frac{\\pi}{4} \\qquad\\textbf{(E)}\\ 1 + \\frac{\\sqrt2}{4} + \\frac{\\pi}{8}$", "description_html": "<p>A unit square is rotated  <span class=\"katex--inline\">45^\\circ</span>  about its center.  What is the area of the region swept out by the interior of the square?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 1 - \\frac{\\sqrt2}{2} + \\frac{\\pi}{4}\\qquad\\textbf{(B)}\\ \\frac{1}{2} + \\frac{\\pi}{4} \\qquad\\textbf{(C)}\\ 2 - \\sqrt2 + \\frac{\\pi}{4}</span> <br/>\n <span class=\"katex--inline\">\\textbf{(D)}\\ \\frac{\\sqrt2}{2} + \\frac{\\pi}{4} \\qquad\\textbf{(E)}\\ 1 + \\frac{\\sqrt2}{4} + \\frac{\\pi}{8}</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": "2013 AMC 10A Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc10A_p21", "prev": "/problem/13_amc10A_p19"}}