{"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":"98dde868-1fcf-575f-9ecf-396b77403436","task_key":"prealgebra--test--98dde868-1fcf-575f-9ecf-396b77403436","task_revision_id":"1","upstream_id":"","short_description":"Side $CD$ of rectangle $ABCD$ measures 12 meters, as shown. Each of the three…","config":"prealgebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Side $CD$ of rectangle $ABCD$ measures 12 meters, as shown. Each of the three triangles with a side along segment $CD$ is an equilateral triangle. What is the total area of the shaded regions? Express your answer in simplest radical form. [asy]\\nimport olympiad; size(150); defaultpen(linewidth(0.8));\\nfill((2,2*sqrt(3))--(4,0)--(6,2*sqrt(3))--cycle^^(6,2*sqrt(3))--(8,0)--(10,2*sqrt(3))--cycle,gray(0.7));\\ndraw((0,0)--(12,0)--(12,2*sqrt(3))--(0,2*sqrt(3))--cycle);\\ndraw((0,0)--(2,2*sqrt(3))--(4,0)--(6,2*sqrt(3))--(8,0)--(10,2*sqrt(3))--(12,0));\\nlabel(\\\"$A$\\\",(0,2*sqrt(3)),NW); label(\\\"$B$\\\",(12,2*sqrt(3)),NE); label(\\\"$C$\\\",(12,0),SE); label(\\\"$D$\\\",(0,0),SW);\\ndraw(\\\"12 meters\\\", (0,2*sqrt(3) + 1)--(12,2*sqrt(3) + 1),N);\\n[/asy]\",\"type\":\"Prealgebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}