{"id":1302,"date":"2020-08-16T23:06:15","date_gmt":"2020-08-16T21:06:15","guid":{"rendered":"http:\/\/matma.com.pl\/?p=1302"},"modified":"2020-08-25T20:24:09","modified_gmt":"2020-08-25T18:24:09","slug":"ostroslupy","status":"publish","type":"post","link":"http:\/\/matma.com.pl\/?p=1302","title":{"rendered":"Ostros\u0142upy"},"content":{"rendered":"<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"color: #4472c4;\"><strong>Ostros\u0142up<\/strong><\/span> jest to bry\u0142a, kt\u00f3ra posiada jedn\u0105 podstaw\u0119, a \u015bciany boczne ostros\u0142upa s\u0105 tr\u00f3jk\u0105tami. W podstawie mo\u017ce znale\u017a\u0107 si\u0119 dowolny wielok\u0105t.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\" wp-image-1305 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/ostros\u0142up-186x300.png\" alt=\"\" width=\"141\" height=\"227\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/ostros\u0142up-186x300.png 186w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/ostros\u0142up.png 233w\" sizes=\"(max-width: 141px) 100vw, 141px\" \/><\/span><\/p>\n<p><span style=\"text-decoration: underline;\"><span style=\"font-family: 'book antiqua', palatino, serif;\">W ka\u017cdym ostros\u0142upie mamy:<\/span><\/span><\/p>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">jedn\u0105 postaw\u0119;<\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">\u015bciany boczne;<\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">odcinek, kt\u00f3ry \u0142\u0105czy wierzcho\u0142ek ostros\u0142upa z p\u0142aszczyzn\u0105 podstawy i jest do niej prostopad\u0142y nazywamy <strong><span style=\"color: #4472c4;\">wysoko\u015bci\u0105 ostros\u0142upa<\/span>.<\/strong><\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img fetchpriority=\"high\" decoding=\"async\" class=\"wp-image-1306 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/ostros\u0142up-opis-300x250.png\" alt=\"\" width=\"338\" height=\"282\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/ostros\u0142up-opis-300x250.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/ostros\u0142up-opis.png 592w\" sizes=\"(max-width: 338px) 100vw, 338px\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Ostros\u0142up, kt\u00f3rego wszystkie \u015bciany (r\u00f3wnie\u017c podstawa) s\u0105 tr\u00f3jk\u0105tami r\u00f3wnobocznymi nosi nazw\u0119 <span style=\"color: #4472c4;\"><strong>czworo\u015bcian foremny<\/strong><\/span>.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"wp-image-1310 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/czworo\u015bcian-300x278.png\" alt=\"\" width=\"181\" height=\"168\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/czworo\u015bcian-300x278.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/czworo\u015bcian.png 330w\" sizes=\"(max-width: 181px) 100vw, 181px\" \/><\/span><\/p>\n<p><span style=\"color: #4472c4;\"><strong><span style=\"font-family: 'book antiqua', palatino, serif;\">Ostros\u0142up tr\u00f3jk\u0105tny<\/span><\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1312 alignleft\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/ostros\u0142up-tr\u00f3jk\u0105tny-232x300.png\" alt=\"\" width=\"155\" height=\"201\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/ostros\u0142up-tr\u00f3jk\u0105tny-232x300.png 232w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/ostros\u0142up-tr\u00f3jk\u0105tny.png 274w\" sizes=\"(max-width: 155px) 100vw, 155px\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">\u015bciany boczne: 3<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">kraw\u0119dzie: 6<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">wierzcho\u0142ki: 4<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">podstawa: tr\u00f3jk\u0105t<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"color: #4472c4;\"><strong><span style=\"font-family: 'book antiqua', palatino, serif;\">Ostros\u0142up czworok\u0105tny\u00a0<\/span><\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1313 alignleft\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/ostros\u0142up-czworokatny-264x300.png\" alt=\"\" width=\"150\" height=\"171\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/ostros\u0142up-czworokatny-264x300.png 264w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/ostros\u0142up-czworokatny.png 337w\" sizes=\"(max-width: 150px) 100vw, 150px\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">\u015bciany boczne: 4<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">kraw\u0119dzie: 8<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">wierzcho\u0142ki: 5<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">podstawa: czworok\u0105t<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><strong><span style=\"color: #4472c4;\">Ostros\u0142up pi\u0119ciok\u0105tny<\/span><\/strong>\u00a0<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1314 alignleft\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/ostros\u0142up-pi\u0119ciok\u0105tny-276x300.png\" alt=\"\" width=\"177\" height=\"192\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/ostros\u0142up-pi\u0119ciok\u0105tny-276x300.png 276w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/ostros\u0142up-pi\u0119ciok\u0105tny.png 321w\" sizes=\"(max-width: 177px) 100vw, 177px\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">\u015bciany boczne: 5<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">kraw\u0119dzie: 10<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">wierzcho\u0142ki: 6<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">podstawa: pi\u0119ciok\u0105t<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><strong><span style=\"color: #4472c4;\">Ostros\u0142up sze\u015bciok\u0105tny<\/span><\/strong>\u00a0<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1315 alignleft\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/ostros\u0142up-sze\u015bciok\u0105tny-206x300.png\" alt=\"\" width=\"155\" height=\"226\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/ostros\u0142up-sze\u015bciok\u0105tny-206x300.png 206w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/ostros\u0142up-sze\u015bciok\u0105tny.png 246w\" sizes=\"(max-width: 155px) 100vw, 155px\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">\u015bciany boczne: 5<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">kraw\u0119dzie: 12<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">wierzcho\u0142ki: 7<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">podstawa: sze\u015bciok\u0105t<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Aby obliczy\u0107\u00a0<span style=\"color: #4472c4;\"><strong>pole powierzchni ca\u0142kowitej ostros\u0142upa<\/strong><\/span> musimy doda\u0107 do siebie pola wszystkich \u015bcian ostros\u0142upa. Tak wi\u0119c jest to suma pola podstawy oraz wszystkich \u015bcian bocznych.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?P_{C}=&amp;space;P_{P}+P_{B}\" alt=\"P_{C}= P_{P}+P_{B}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?P_{P}\" alt=\"P_{P}\" align=\"absmiddle\" \/>\u00a0to pole powierzchni podstawy<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?P_{B}\" alt=\"P_{B}\" align=\"absmiddle\" \/> to pole powierzchni bocznej, czyli suma p\u00f3l wszystkich \u015bcian bocznych.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ostros\u0142up jest to bry\u0142a, kt\u00f3ra posiada jedn\u0105 podstaw\u0119, a \u015bciany boczne ostros\u0142upa s\u0105 tr\u00f3jk\u0105tami. W podstawie mo\u017ce znale\u017a\u0107 si\u0119 dowolny wielok\u0105t. W ka\u017cdym ostros\u0142upie mamy: jedn\u0105 postaw\u0119; \u015bciany boczne; odcinek, kt\u00f3ry \u0142\u0105czy wierzcho\u0142ek ostros\u0142upa z p\u0142aszczyzn\u0105 podstawy i jest do niej prostopad\u0142y nazywamy wysoko\u015bci\u0105 ostros\u0142upa. Ostros\u0142up, kt\u00f3rego wszystkie \u015bciany (r\u00f3wnie\u017c podstawa) s\u0105 tr\u00f3jk\u0105tami r\u00f3wnobocznymi nosi [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,13],"tags":[],"class_list":["post-1302","post","type-post","status-publish","format-standard","hentry","category-baza-wiedzy","category-klasa-vi"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Ostros\u0142upy - Matma.com.pl<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/matma.com.pl\/?p=1302\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Ostros\u0142upy - Matma.com.pl\" \/>\n<meta property=\"og:description\" content=\"Ostros\u0142up jest to bry\u0142a, kt\u00f3ra posiada jedn\u0105 podstaw\u0119, a \u015bciany boczne ostros\u0142upa s\u0105 tr\u00f3jk\u0105tami. W podstawie mo\u017ce znale\u017a\u0107 si\u0119 dowolny wielok\u0105t. W ka\u017cdym ostros\u0142upie mamy: jedn\u0105 postaw\u0119; \u015bciany boczne; odcinek, kt\u00f3ry \u0142\u0105czy wierzcho\u0142ek ostros\u0142upa z p\u0142aszczyzn\u0105 podstawy i jest do niej prostopad\u0142y nazywamy wysoko\u015bci\u0105 ostros\u0142upa. 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