{"id":"cb_question_bank:fe0a4dd4-f49a-4978-96ae-b6ea3c2fdfc2","source_id":"cb_question_bank","source_item_id":"fe0a4dd4-f49a-4978-96ae-b6ea3c2fdfc2","external_id":null,"ibn":"038021-DC","question_id":"cf53cb56","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.A.","skill":"Area and volume","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In the xy -plane shown, square ABCD has its diagonals on the x - and y -axes. What is the area, in square units, of the square?","stimulus":"The figure presents the graph of square A B C D in the x y plane. The numbers negative 5 and 5 are indicated on each axis. The coordinates of each vertex are as follows. Vertex A has coordinates 0 comma negative 5. Vertex B has coordinates negative 5 comma 0. Vertex C has coordinates 0 comma 5. Vertex D has coordinates 5 comma 0.","stimulus_html":"<div class=\"stimulus_reference \">\n        <div class=\"standalone_image \">\n          <img src=\"/api/assets/53933d5933c08233ce355282cc91f5841c5c5f0d23352f74130050f96de53da2\" alt=\"The figure presents the graph of square A B C D in the x y plane. The numbers negative 5 and 5 are indicated on each axis. The coordinates of each vertex are as follows.\nVertex A has coordinates 0 comma negative 5.\nVertex B has coordinates negative 5 comma 0.\nVertex C has coordinates 0 comma 5.\nVertex D has coordinates 5 comma 0.\n\" width=\"139\" height=\"144\"></div>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">In the <span class=\"italic \">xy</span>-plane shown, square <span class=\"italic\">ABCD</span> has its diagonals on the <span class=\"italic \">x</span>- and <span class=\"italic \">y</span>-axes. What is the area, in&nbsp;square units, of the square?</p>\n","rationale_html":"<p>Choice C is correct. The two diagonals of square <span class=\"italic\">ABCD</span> divide the square into 4 congruent right triangles, where each triangle has a vertex at the origin of the graph shown. The formula for the area of a triangle is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a846c48c643fad31f9ef1ac9980c0bff81b404b57d80bb3aa19357242ec48174\" alt=\"A equals, one half times b h\"></span>, where <span class=\"italic\">b</span> is the base length of the triangle and <span class=\"italic\">h</span> is the height of the triangle. Each of the 4 congruent right triangles has a height of 5 units and a base length of 5 units. Therefore, the area of each triangle is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f60f2df4c7cb13dc6b7a65b363bdf457657f2f2e9da8181ebaa054dcfced0e32\" alt=\"A equals, one half times, 5 times 5\"></span>, or 12.5 square units. Since the 4 right triangles are congruent, the area of each is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c2cdda43637be35379a891f9cbba6a665ae6aa43f563929757acf84127e4bcef\" alt=\"one fourth \"></span> of the area of square <span class=\"italic\">ABCD</span>. It follows that the area of the square <span class=\"italic\">ABCD</span> is equal to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f4227f0570bf662ff0de7934b9e15267077c114612595b51e598616e6d7242df\" alt=\"4 times 12 point 5\"></span>, or 50 square units.</p><p>Choices A and D are incorrect and may result from using 5 or 25, respectively, as the area of one of the 4 congruent right triangles formed by diagonals of square <span class=\"italic\">ABCD</span>. However, the area of these triangles is 12.5. Choice B is incorrect and may result from using 5 as the length of one side of square <span class=\"italic\">ABCD</span>. However, the length of a side of square <span class=\"italic\">ABCD</span> is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/98e109182266d5f504a8e103b8015a539bb5a9388178cd7a9880d62dadeefde5\" alt=\"5 times the square root of 2\"></span>.</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.627000+00:00","source_updated_at":"2023-08-02T20:25:59.627000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">20</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">25</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">50</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">100</p>\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}