{"status": "success", "data": {"description_md": "On each side of a unit square, an equilateral triangle of side length 1 is constructed. On each new side of each equilateral triangle, another equilateral triangle of side length 1 is constructed. The interiors of the square and the 12 triangles have no points in common. Let $R$ be the region formed by the union of the square and all the triangles, and $S$ be the smallest convex polygon that contains $R$. What is the area of the region that is inside $S$ but outside $R$?\n\n$\\textbf{(A)} \\; \\frac {1}{4} \\qquad \\textbf{(B)} \\; \\frac {\\sqrt {2}}{4} \\qquad \\textbf{(C)} \\; 1 \\qquad \\textbf{(D)} \\; \\sqrt {3} \\qquad \\textbf{(E)} \\; 2 \\sqrt {3}$<br>([[2008 AMC 12B Problems/Problem 15|Solution]])\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": "<p>On each side of a unit square, an equilateral triangle of side length 1 is constructed. On each new side of each equilateral triangle, another equilateral triangle of side length 1 is constructed. The interiors of the square and the 12 triangles have no points in common. Let  <span class=\"katex--inline\">R</span>  be the region formed by the union of the square and all the triangles, and  <span class=\"katex--inline\">S</span>  be the smallest convex polygon that contains  <span class=\"katex--inline\">R</span> . What is the area of the region that is inside  <span class=\"katex--inline\">S</span>  but outside  <span class=\"katex--inline\">R</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)} \\; \\frac {1}{4} \\qquad \\textbf{(B)} \\; \\frac {\\sqrt {2}}{4} \\qquad \\textbf{(C)} \\; 1 \\qquad \\textbf{(D)} \\; \\sqrt {3} \\qquad \\textbf{(E)} \\; 2 \\sqrt {3}</span> <br/>([[2008 AMC 12B Problems/Problem 15|Solution]])</p>&#10;<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": "2008 AMC 12B Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc12B_p16", "prev": "/problem/08_amc12B_p14"}}