{"status": "success", "data": {"description_md": "Let points $A = (0 ,0 ,0)$, $B = (1, 0, 0)$, $C = (0, 2, 0)$, and $D = (0, 0, 3)$. Points $E$, $F$, $G$, and $H$ are midpoints of line segments $\\overline{BD},\\text{ }  \\overline{AB}, \\text{ } \\overline {AC},$ and $\\overline{DC}$ respectively. What is the area of $EFGH$?\n\n$\\textbf{(A)}\\ \\sqrt{2}\\qquad\\textbf{(B)}\\ \\frac{2\\sqrt{5}}{3}\\qquad\\textbf{(C)}\\ \\frac{3\\sqrt{5}}{4}\\qquad\\textbf{(D)}\\ \\sqrt{3}\\qquad\\textbf{(E)}\\ \\frac{2\\sqrt{7}}{3}$", "description_html": "<p>Let points  <span class=\"katex--inline\">A = (0 ,0 ,0)</span> ,  <span class=\"katex--inline\">B = (1, 0, 0)</span> ,  <span class=\"katex--inline\">C = (0, 2, 0)</span> , and  <span class=\"katex--inline\">D = (0, 0, 3)</span> . Points  <span class=\"katex--inline\">E</span> ,  <span class=\"katex--inline\">F</span> ,  <span class=\"katex--inline\">G</span> , and  <span class=\"katex--inline\">H</span>  are midpoints of line segments  <span class=\"katex--inline\">\\overline{BD},\\text{ }  \\overline{AB}, \\text{ } \\overline {AC},</span>  and  <span class=\"katex--inline\">\\overline{DC}</span>  respectively. What is the area of  <span class=\"katex--inline\">EFGH</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\sqrt{2}\\qquad\\textbf{(B)}\\ \\frac{2\\sqrt{5}}{3}\\qquad\\textbf{(C)}\\ \\frac{3\\sqrt{5}}{4}\\qquad\\textbf{(D)}\\ \\sqrt{3}\\qquad\\textbf{(E)}\\ \\frac{2\\sqrt{7}}{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": "2012 AMC 10A Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/12_amc10A_p22", "prev": "/problem/12_amc10A_p20"}}