{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"9e0841e6-375b-5a57-b089-89cd49a56d52","task_key":"geometry--test--9e0841e6-375b-5a57-b089-89cd49a56d52","task_revision_id":"1","upstream_id":"","short_description":"All of the triangles in the figure and the central hexagon are equilateral.…","config":"geometry","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"All of the triangles in the figure and the central hexagon are equilateral. Given that $\\\\overline{AC}$ is 3 units long, how many square units, expressed in simplest radical form, are in the area of the entire star? [asy]\\nimport olympiad; import geometry; import graph; size(150); defaultpen(linewidth(0.8));\\npair[] vertices;\\nfor(int i = 0; i < 6; ++i){\\n\\nvertices[i] = dir(30 + 60*i);\\n}\\ndraw(vertices[0]--vertices[2]--vertices[4]--cycle);\\ndraw(vertices[1]--vertices[3]--vertices[5]--cycle);\\nlabel(\\\"$D$\\\",vertices[0],NE); label(\\\"$C$\\\",vertices[1],N); label(\\\"$B$\\\",vertices[2],NW); label(\\\"$A$\\\",vertices[3],SW);\\nlabel(\\\"$F$\\\",vertices[4],S); label(\\\"$E$\\\",vertices[5],SE);\\n[/asy]\",\"type\":\"Geometry\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}