{"status": "success", "data": {"description_md": "In rectangle $ABCD$, $AB=1$, $BC=2$, and points $E$, $F$, and $G$ are midpoints of $\\overline{BC}$, $\\overline{CD}$, and $\\overline{AD}$, respectively. Point $H$ is the midpoint of $\\overline{GE}$. What is the area of the shaded region?\n\n<center>\n<img class=\"problem-image\" height=\"428\" src=\"https://latex.artofproblemsolving.com/1/2/5/12524bb96209b0c956b2060192deb8429c73e3f3.png\" width=\"232\"/>\n</center>\n\n$\\textbf{(A)}\\ \\dfrac1{12}\\qquad\\textbf{(B)}\\ \\dfrac{\\sqrt3}{18}\\qquad\\textbf{(C)}\\ \\dfrac{\\sqrt2}{12}\\qquad\\textbf{(D)}\\ \\dfrac{\\sqrt3}{12}\\qquad\\textbf{(E)}\\ \\dfrac16$", "description_html": "<p>In rectangle  <span class=\"katex--inline\">ABCD</span> ,  <span class=\"katex--inline\">AB=1</span> ,  <span class=\"katex--inline\">BC=2</span> , and points  <span class=\"katex--inline\">E</span> ,  <span class=\"katex--inline\">F</span> , and  <span class=\"katex--inline\">G</span>  are midpoints of  <span class=\"katex--inline\">\\overline{BC}</span> ,  <span class=\"katex--inline\">\\overline{CD}</span> , and  <span class=\"katex--inline\">\\overline{AD}</span> , respectively. Point  <span class=\"katex--inline\">H</span>  is the midpoint of  <span class=\"katex--inline\">\\overline{GE}</span> . What is the area of the shaded region?</p>\n<center>\n<img class=\"problem-image\" height=\"428\" src=\"https://latex.artofproblemsolving.com/1/2/5/12524bb96209b0c956b2060192deb8429c73e3f3.png\" width=\"232\"/>\n</center>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\dfrac1{12}\\qquad\\textbf{(B)}\\ \\dfrac{\\sqrt3}{18}\\qquad\\textbf{(C)}\\ \\dfrac{\\sqrt2}{12}\\qquad\\textbf{(D)}\\ \\dfrac{\\sqrt3}{12}\\qquad\\textbf{(E)}\\ \\dfrac16</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": "2014 AMC 10A Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/14_amc10A_p17", "prev": "/problem/14_amc10A_p15"}}