{"id":1589,"date":"2020-09-02T15:44:05","date_gmt":"2020-09-02T13:44:05","guid":{"rendered":"http:\/\/matma.com.pl\/?p=1589"},"modified":"2020-09-02T17:08:00","modified_gmt":"2020-09-02T15:08:00","slug":"ostroslupy-2","status":"publish","type":"post","link":"http:\/\/matma.com.pl\/?p=1589","title":{"rendered":"Ostros\u0142upy"},"content":{"rendered":"<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"color: #4472c4;\"><strong>Ostros\u0142up<\/strong><\/span>\u00a0jest 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 fetchpriority=\"high\" decoding=\"async\" class=\"size-medium wp-image-1306 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/ostros\u0142up-opis-300x250.png\" alt=\"\" width=\"300\" height=\"250\" 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: 300px) 100vw, 300px\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"text-decoration: underline;\">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\u00a0<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;\">Wsp\u00f3lny punkt wysoko\u015bci ostros\u0142upa i p\u0142aszczyzny podstawy to <span style=\"color: #4472c4;\"><strong>spodek wysoko\u015bci<\/strong><\/span>.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"wp-image-1594 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/wysoko\u015b\u0107-ostros\u0142upa-300x274.png\" alt=\"\" width=\"311\" height=\"284\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/wysoko\u015b\u0107-ostros\u0142upa-300x274.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/wysoko\u015b\u0107-ostros\u0142upa.png 503w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"color: #4472c4;\"><strong>Ostros\u0142up<\/strong><\/span> mo\u017ce by\u0107 tak\u017ce <span style=\"color: #4472c4;\"><strong>pochy\u0142y<\/strong><\/span> w\u00f3wczas spodek wysoko\u015bci takiego ostros\u0142upa nie le\u017cy w jego podstawie.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"size-medium wp-image-1596 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/ostros\u0142up-spodek-poza-podstawa-300x200.png\" alt=\"\" width=\"300\" height=\"200\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/ostros\u0142up-spodek-poza-podstawa-300x200.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/ostros\u0142up-spodek-poza-podstawa.png 376w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><span style=\"color: #4472c4;\"><strong>Ostros\u0142up prawid\u0142owy<\/strong><\/span> to taki ostros\u0142up, kt\u00f3ry ma w podstawie wielok\u0105t foremny a kraw\u0119dzie \u015bcian bocznych s\u0105 takiej samej d\u0142ugo\u015bci.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1597 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/ostros\u0142up-prawid\u0142owy-228x300.png\" alt=\"\" width=\"212\" height=\"279\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/ostros\u0142up-prawid\u0142owy-228x300.png 228w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/ostros\u0142up-prawid\u0142owy-285x377.png 285w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/ostros\u0142up-prawid\u0142owy.png 287w\" sizes=\"(max-width: 212px) 100vw, 212px\" \/><\/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\u00a0<span style=\"color: #4472c4;\"><strong>czworo\u015bcian foremny<\/strong><\/span>.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-1600 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/ostr2-267x300.png\" alt=\"\" width=\"267\" height=\"300\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/ostr2-267x300.png 267w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/ostr2.png 269w\" sizes=\"(max-width: 267px) 100vw, 267px\" \/><\/span><\/p>\n<p><span style=\"text-decoration: underline; font-family: 'book antiqua', palatino, serif;\">Przyk\u0142adowe siatki ostros\u0142up\u00f3w:<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1598\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/ostr1-192x300.png\" alt=\"\" width=\"143\" height=\"223\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/ostr1-192x300.png 192w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/ostr1.png 239w\" sizes=\"(max-width: 143px) 100vw, 143px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1599\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/siatka-ostr1-268x300.png\" alt=\"\" width=\"276\" height=\"309\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/siatka-ostr1-268x300.png 268w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/siatka-ostr1.png 619w\" sizes=\"(max-width: 276px) 100vw, 276px\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1600\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/ostr2-267x300.png\" alt=\"\" width=\"221\" height=\"248\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/ostr2-267x300.png 267w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/ostr2.png 269w\" sizes=\"(max-width: 221px) 100vw, 221px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1601\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/siatka-ostr2-300x256.png\" alt=\"\" width=\"296\" height=\"253\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/siatka-ostr2-300x256.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/siatka-ostr2.png 397w\" sizes=\"(max-width: 296px) 100vw, 296px\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1602\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/ostr3-244x300.png\" alt=\"\" width=\"174\" height=\"214\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/ostr3-244x300.png 244w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/ostr3.png 264w\" sizes=\"(max-width: 174px) 100vw, 174px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1603\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/siatka-ostr3-266x300.png\" alt=\"\" width=\"315\" height=\"355\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/siatka-ostr3-266x300.png 266w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/09\/siatka-ostr3.png 577w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><\/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>\u00a0<\/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\" \/>\u00a0to pole powierzchni bocznej, czyli suma p\u00f3l wszystkich \u015bcian bocznych.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><strong><span style=\"color: #4472c4;\">Obj\u0119to\u015b\u0107 ostros\u0142upa<\/span>, <\/strong>to jedna trzecia obj\u0119to\u015bci graniastos\u0142upa o takiej samej podstawie.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"aligncenter\" src=\"http:\/\/latex.codecogs.com\/gif.latex?V=\\frac{1}{3}P_{P}\\cdot&amp;space;H\" alt=\"V=\\frac{1}{3}P_{P}\\cdot H\" 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?H\" alt=\"H\" align=\"absmiddle\" \/>\u00a0to wysoko\u015b\u0107 graniastos\u0142upa.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ostros\u0142up\u00a0jest 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\u00a0wysoko\u015bci\u0105 ostros\u0142upa. Wsp\u00f3lny punkt wysoko\u015bci ostros\u0142upa i p\u0142aszczyzny podstawy to spodek wysoko\u015bci. Ostros\u0142up mo\u017ce [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,15],"tags":[],"class_list":["post-1589","post","type-post","status-publish","format-standard","hentry","category-baza-wiedzy","category-klasa-viii"],"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=\"https:\/\/matma.com.pl\/?p=1589\" \/>\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\u00a0jest 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\u00a0wysoko\u015bci\u0105 ostros\u0142upa. Wsp\u00f3lny punkt wysoko\u015bci ostros\u0142upa i p\u0142aszczyzny podstawy to spodek wysoko\u015bci. 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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\u00a0wysoko\u015bci\u0105 ostros\u0142upa. Wsp\u00f3lny punkt wysoko\u015bci ostros\u0142upa i p\u0142aszczyzny podstawy to spodek wysoko\u015bci. 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