{"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 algebra / test selection.","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":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"a3905f9a-900c-556d-b81e-0118c299cd6f","task_key":"algebra--test--a3905f9a-900c-556d-b81e-0118c299cd6f","task_revision_id":"2","upstream_id":"","short_description":"Kite $ABCD$ (a quadrilateral with two pairs of adjacent equal sides) has…","config":"algebra","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"Kite $ABCD$ (a quadrilateral with two pairs of adjacent equal sides) has coordinates $A\\\\ (0,7),\\\\ B\\\\ (1,0),\\\\ C\\\\ (12,-2),$ and $D\\\\ (7,8).$ What is the area of $ABCD,$ given that the area of a kite is equal to half the product of its diagonals?\\n\\n[asy]\\nstring sp(pair P, string P2){return \\\"$\\\" + P2 + \\\"\\\\,(\\\" + string(P.x) + \\\",\\\" + string(P.y) + \\\")$\\\";}\\nsize(150); defaultpen(fontsize(10)); draw((-5,0)--(15,0),Arrows(4)); draw((0,-5)--(0,10),Arrows(4)); pair A=(0,7),B=(1,0),C=(12,-2),D=(7,8); draw(A--B--C--D--cycle, linewidth(0.7)); draw(A--C, dashed); draw(B--D, dashed); label(sp(A,\\\"A\\\"),A,W); label(sp(B,\\\"B\\\"),B,S); label(sp(C,\\\"C\\\"),C,E); label(sp(D,\\\"D\\\"),D,N);\\n[/asy]\",\"type\":\"Algebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}