{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-05-26T00:16:20.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-05-26T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":60566,"title":"Given a Polyshape_01 (ps) Return its Perimeter, Area, and Centroid.","description":"Return the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\r\nReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\r\nReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. ","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 52.3333px; transform-origin: 407.5px 52.3333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.8333px; text-align: left; transform-origin: 384.5px 10.8333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.3333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21.6667px; text-align: left; transform-origin: 384.5px 21.6667px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.8333px; text-align: left; transform-origin: 384.5px 10.8333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"%%\r\nfunction [P, A, Cx, Cy] = PolyShape_01(ps)\r\n    % Return the perimeter (P) of a polyshape object, which is the sum\r\n    % of the lengths of its boundaries.\r\n    \r\n    % Return the total area (A) of a polyshape object, which is the sum\r\n    % of the areas of the solid regions that make up the polyshape.\r\n    \r\n    % Return the x-coordinate (Cx) and the y-coordinate (Cy) of the\r\n    % centroid of a polyshape. \r\n end","test_suite":"%% Test 1\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),1313))\r\n    assert(isequal(round(A,4),134508.0227))\r\n    assert(isequal(round(Cx,4),17))\r\n    assert(isequal(round(Cy,4),47))\r\n\r\n    \r\n%% Test 2\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),1313))\r\n    assert(isequal(round(A,4),134508.0227))\r\n    assert(isequal(round(Cx,4),254))\r\n    assert(isequal(round(Cy,4),-1676))\r\n\r\n    \r\n%% Test 3\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),177.255))\r\n    assert(isequal(round(A,4),2451.4087))\r\n    assert(isequal(round(Cx,4),34.29 ))\r\n    assert(isequal(round(Cy,4),-226.26))\r\n\r\n    \r\n%% Test 4\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),206.155))\r\n    assert(isequal(round(A,4),2385.7031))\r\n    assert(isequal(round(Cx,4),34.0501))\r\n    assert(isequal(round(Cy,4),-226.4324))\r\n\r\n    \r\n%% Test 5\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[20, -220],'SideLength', 1.7));\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),235.055))\r\n    assert(isequal(round(A,4),2319.9976))\r\n    assert(isequal(round(Cx,4),34.448))\r\n    assert(isequal(round(Cy,4),-226.6146))\r\n\r\n    \r\n%% Test 6\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[20, -220],'SideLength', 1.7));\r\n    ps = subtract(ps,polyshape([20 30.1 40.1 45.1 50 45.2 40.2 30.2 27.2],[-235 -239 -239 -237 -235 -239 -241 -240.5 -240]));\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),300.0489))\r\n    assert(isequal(round(A,4),2274.2476))\r\n    assert(isequal(round(Cx,4),34.4235))\r\n    assert(isequal(round(Cy,4),-226.367))\r\n    \r\n    \r\n    ","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":20795,"edited_by":20795,"edited_at":"2024-06-28T13:41:58.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-06-26T18:00:30.000Z","updated_at":"2026-03-18T15:16:22.000Z","published_at":"2024-06-26T18:18:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts 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","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 104.667px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 52.3333px; transform-origin: 407.5px 52.3333px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.8333px; text-align: left; transform-origin: 384.5px 10.8333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the perimeter (P) of a polyshape object, which is the sum of the lengths of its boundaries.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 43.3333px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 21.6667px; text-align: left; transform-origin: 384.5px 21.6667px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the total area (A) of a polyshape object, which is the sum of the areas of the solid regions that make up the polyshape.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21.6667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384.5px 10.8333px; text-align: left; transform-origin: 384.5px 10.8333px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eReturn the x-coordinate (Cx) and the y-coordinate (Cy) of the centroid of a polyshape. \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"%%\r\nfunction [P, A, Cx, Cy] = PolyShape_01(ps)\r\n    % Return the perimeter (P) of a polyshape object, which is the sum\r\n    % of the lengths of its boundaries.\r\n    \r\n    % Return the total area (A) of a polyshape object, which is the sum\r\n    % of the areas of the solid regions that make up the polyshape.\r\n    \r\n    % Return the x-coordinate (Cx) and the y-coordinate (Cy) of the\r\n    % centroid of a polyshape. \r\n end","test_suite":"%% Test 1\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),1313))\r\n    assert(isequal(round(A,4),134508.0227))\r\n    assert(isequal(round(Cx,4),17))\r\n    assert(isequal(round(Cy,4),47))\r\n\r\n    \r\n%% Test 2\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),1313))\r\n    assert(isequal(round(A,4),134508.0227))\r\n    assert(isequal(round(Cx,4),254))\r\n    assert(isequal(round(Cy,4),-1676))\r\n\r\n    \r\n%% Test 3\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),177.255))\r\n    assert(isequal(round(A,4),2451.4087))\r\n    assert(isequal(round(Cx,4),34.29 ))\r\n    assert(isequal(round(Cy,4),-226.26))\r\n\r\n    \r\n%% Test 4\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),206.155))\r\n    assert(isequal(round(A,4),2385.7031))\r\n    assert(isequal(round(Cx,4),34.0501))\r\n    assert(isequal(round(Cy,4),-226.4324))\r\n\r\n    \r\n%% Test 5\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[20, -220],'SideLength', 1.7));\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),235.055))\r\n    assert(isequal(round(A,4),2319.9976))\r\n    assert(isequal(round(Cx,4),34.448))\r\n    assert(isequal(round(Cy,4),-226.6146))\r\n\r\n    \r\n%% Test 6\r\n    ps = nsidedpoly(13,'Center',[17, 47],'SideLength', 101);\r\n    ps = translate(ps,[237,-1723]);\r\n    ps = scale(ps,0.135);\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[43, -220],'SideLength', 1.7));\r\n    ps = subtract(ps,nsidedpoly(17,'Center',[20, -220],'SideLength', 1.7));\r\n    ps = subtract(ps,polyshape([20 30.1 40.1 45.1 50 45.2 40.2 30.2 27.2],[-235 -239 -239 -237 -235 -239 -241 -240.5 -240]));\r\n    [P, A, Cx, Cy] = PolyShape_01(ps);\r\n    assert(isequal(round(P,4),300.0489))\r\n    assert(isequal(round(A,4),2274.2476))\r\n    assert(isequal(round(Cx,4),34.4235))\r\n    assert(isequal(round(Cy,4),-226.367))\r\n    \r\n    \r\n    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