{"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":"5ba3ff0d-78fe-5515-b6b8-f7577d4fb430","task_key":"geometry--test--5ba3ff0d-78fe-5515-b6b8-f7577d4fb430","task_revision_id":"1","upstream_id":"","short_description":"Three congruent isosceles triangles $DAO$, $AOB$ and $OBC$ have $AD=AO=OB=BC=10$…","config":"geometry","split":"test","body":"{\"level\":\"Level 2\",\"problem\":\"Three congruent isosceles triangles $DAO$, $AOB$ and $OBC$ have $AD=AO=OB=BC=10$ and $AB=DO=OC=12$.  These triangles are arranged to form trapezoid $ABCD$, as shown.  Point $P$ is on side $AB$ so that $OP$ is perpendicular to $AB$.\\n\\n[asy]\\n\\npair A, B, C, D, O, P;\\n\\nA= (6, 8);\\n\\nB=(18, 8);\\n\\nC=(24, 0);\\n\\nD=(0,0);\\n\\nO=(12,0);\\n\\nP=(12,8);\\n\\ndraw(A--B--C--D--A);\\n\\ndraw(A--O--B);\\n\\ndraw(O--P, dashed);\\n\\nlabel(\\\"A\\\", A, NW);\\n\\nlabel(\\\"B\\\", B, NE);\\n\\nlabel(\\\"C\\\", C, SE);\\n\\nlabel(\\\"D\\\", D, SW);\\n\\nlabel(\\\"O\\\", O, S);\\n\\nlabel(\\\"P\\\", P, N);\\n\\nlabel(\\\"12\\\", (D+O)/2, S);\\n\\nlabel(\\\"12\\\", (O+C)/2, S);\\n\\nlabel(\\\"10\\\", (A+D)/2, NW);\\n\\nlabel(\\\"10\\\", (B+C)/2, NE);\\n\\n[/asy]\\n\\nWhat is the area of trapezoid $ABCD$?\",\"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":[]}