{"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":"4a439693-2daa-50bc-9663-f92eec8de0f5","task_key":"geometry--test--4a439693-2daa-50bc-9663-f92eec8de0f5","task_revision_id":"1","upstream_id":"","short_description":"A rectangular piece of paper $ABCD$ is folded so that edge $CD$ lies along edge…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"A rectangular piece of paper $ABCD$ is folded so that edge $CD$ lies along edge $AD,$ making a crease $DP.$ It is unfolded, and then folded again so that edge $AB$ lies along edge $AD,$ making a second crease $AQ.$ The two creases meet at $R,$ forming triangles $PQR$ and $ADR$. If $AB=5\\\\mbox{ cm}$ and $AD=8\\\\mbox{ cm},$ what is the area of quadrilateral $DRQC,$ in $\\\\mbox{cm}^2?$\\n\\n[asy]\\nsize(250);\\ndraw((0,0)--(5,0)--(5,8)--(0,8)--cycle,black+linewidth(1));\\ndraw((8,0)--(8,8)--(13,8)--(13,5)--(8,5),black+linewidth(1));\\ndraw((8,0)--(13,5),black+linewidth(1)+dashed);\\ndraw((16,0)--(21,0)--(21,8)--(16,8)--cycle,black+linewidth(1));\\ndraw((16,0)--(21,5),black+linewidth(1)+dashed);\\ndraw((16,8)--(21,3),black+linewidth(1)+dashed);\\ndraw((12,0)--(10,2),black+linewidth(1));\\ndraw((12,0)--(10,2),EndArrow);\\nlabel(\\\"$A$\\\",(0,8),N);\\nlabel(\\\"$B$\\\",(5,8),N);\\nlabel(\\\"$C$\\\",(5,0),S);\\nlabel(\\\"$D$\\\",(0,0),S);\\nlabel(\\\"$A$\\\",(8,8),N);\\nlabel(\\\"$B$\\\",(13,8),N);\\nlabel(\\\"$C$\\\",(8,5),W);\\nlabel(\\\"$D$\\\",(8,0),S);\\nlabel(\\\"$P$\\\",(13,5),E);\\nlabel(\\\"$A$\\\",(16,8),N);\\nlabel(\\\"$B$\\\",(21,8),N);\\nlabel(\\\"$C$\\\",(21,0),S);\\nlabel(\\\"$D$\\\",(16,0),S);\\nlabel(\\\"$P$\\\",(21,5),E);\\nlabel(\\\"$Q$\\\",(21,3),E);\\nlabel(\\\"$R$\\\",(20,4),W);\\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":[]}