{"status": "success", "data": {"description_md": "A cube with side length $1$ is sliced by a plane that passes through two diagonally opposite vertices $A$ and $C$ and the midpoints $B$ and $D$ of two opposite edges not containing $A$ or $C$, as shown. What is the area of quadrilateral $ABCD$?\n\n<center>\n<img class=\"problem-image\" height=\"655\" src=\"https://latex.artofproblemsolving.com/2/e/6/2e6d3b454ada297f5ac1d3f4ab29dd80332b3c72.png\" width=\"658\"/>\n</center>\n\n$\\mathrm{(A)}\\ \\frac{\\sqrt{6}}{2}\\qquad\\mathrm{(B)}\\ \\frac{5}{4}\\qquad\\mathrm{(C)}\\ \\sqrt{2}\\qquad\\mathrm{(D)}\\ \\frac{5}{8}\\qquad\\mathrm{(E)}\\ \\frac{3}{4}$", "description_html": "<p>A cube with side length  <span class=\"katex--inline\">1</span>  is sliced by a plane that passes through two diagonally opposite vertices  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">C</span>  and the midpoints  <span class=\"katex--inline\">B</span>  and  <span class=\"katex--inline\">D</span>  of two opposite edges not containing  <span class=\"katex--inline\">A</span>  or  <span class=\"katex--inline\">C</span> , as shown. What is the area of quadrilateral  <span class=\"katex--inline\">ABCD</span> ?</p>\n<center>\n<img class=\"problem-image\" height=\"655\" src=\"https://latex.artofproblemsolving.com/2/e/6/2e6d3b454ada297f5ac1d3f4ab29dd80332b3c72.png\" width=\"658\"/>\n</center>\n<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ \\frac{\\sqrt{6}}{2}\\qquad\\mathrm{(B)}\\ \\frac{5}{4}\\qquad\\mathrm{(C)}\\ \\sqrt{2}\\qquad\\mathrm{(D)}\\ \\frac{5}{8}\\qquad\\mathrm{(E)}\\ \\frac{3}{4}</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": "2008 AMC 10A Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc10A_p22", "prev": "/problem/08_amc10A_p20"}}