{"id":4749,"date":"2022-09-01T15:06:23","date_gmt":"2022-09-01T13:06:23","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/obsah-trojuhelniku-priklad\/"},"modified":"2022-09-01T15:06:23","modified_gmt":"2022-09-01T13:06:23","slug":"obsah-trojuhelniku-priklad","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/obsah-trojuhelniku-priklad\/","title":{"rendered":"Obsah troj\u00faheln\u00edku &#8211; p\u0159\u00edklad"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:&nbsp;<\/strong><\/p>\n<p style=\"text-align: center\" data-mce-style=\"text-align: center;\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone  wp-image-4748\" src=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/trojuhlenik-300x201.png\" alt=\"\" width=\"490\" height=\"328\" data-mce-src=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/trojuhlenik-300x201.png\" srcset=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/trojuhlenik-300x201.png 300w, https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/trojuhlenik.png 401w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><\/p>\n<p>Je d\u00e1n p\u011bti\u00faheln\u00edk <em><strong>ABCED<\/strong> <\/em>kter\u00fd je slo\u017een ze \u010dtverce <strong><em>ABCD<\/em><\/strong> a troj\u00faheln\u00edku <em><strong>CED<\/strong><\/em>. V\u00edme obsahy \u010dtverce a troj\u00faheln\u00edku:<br \/>$$\u0394 CED = 30 cm^{2}$$<br \/>$$\u25a1 ABCD = 100 cm^{2}$$<br \/>&nbsp; <br \/><strong>Jak\u00fd je obsah troj\u00faheln\u00edku ABE?<\/strong><br \/>A) Men\u0161\u00ed ne\u017e 75 cm\u00b2<br \/>B) 75 cm\u00b2<br \/>C) 78 cm\u00b2<br \/>D) 80 cm\u00b2<br \/>E) V\u011bt\u0161\u00ed ne\u017e 80 cm\u00b2<\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p>1) Pomoc\u00ed vzore\u010dku na obsah \u010dtverce ABCD, vypo\u010d\u00edt\u00e1me d\u00e9lku strany a<br \/>$$S_{\u010d} = a^{2}$$<br \/>2) Dosad\u00edme<br \/>$$100 = a^{2}$$<br \/>3) Nyn\u00ed v\u00edme d\u00e9lku strany a<br \/>$$a = 10 cm$$<br \/>4) Nyn\u00ed stejnou dosazovac\u00ed metodou vyu\u017eijeme p\u0159i v\u00fdpo\u010dtu v\u00fd\u0161ky v troj\u00faheln\u00edku CDE:<br \/>$$S_{DCE}=\\frac{v\\cdot a}{2}$$<br \/>5) Dosad\u00edme<br \/>$$30=\\frac{v\\cdot 10}{2}$$<br \/>6) Nyn\u00ed v\u00edme d\u00e9lku v\u00fd\u0161ky v; zjistili jsme ji tak, \u017ee jsme levou strany p\u0159evedly na stejn\u00e9ho jmenovatele, tedy \u010d\u00edslo jsme vyn\u00e1sobili 2 (\u010ditatelem zlomku); pak u\u017e jsme 10 p\u0159evedli na druhou stranu a t\u00edm p\u00e1dem se n\u00e1m kr\u00e1t prom\u011bnilo v d\u011bleno<br \/>$$v = 6cm$$<br \/>7) Zn\u00e1me ji\u017e v\u0161e pot\u0159ebn\u00e9 pro v\u00fdpo\u010det obsahu troj\u00faheln\u00edku ABE, pou\u017eijeme vzore\u010dek<br \/>$$S_{ABE}=\\frac{v_{c}\\cdot a}{2}$$<br \/>8) Dosad\u00edme (V\u00fd\u0161ku tohoto troj\u00faheln\u00edku z\u00edsk\u00e1me sou\u010dtem d\u00e9lky strany a \u010dtverce a v\u00fd\u0161ky v u troj\u00faheln\u00edku)<br \/>$$S_{ABE}=\\frac{16\\cdot 10}{2}$$<br \/>9) M\u00e1me vypo\u010dten obsah troj\u00faheln\u00edku ABE<br \/>$$S_{ABE}=80 cm^{2}$$<br \/><strong>Spr\u00e1vn\u011b je odpov\u011b\u010f D.<\/strong><\/p>\n<p>\u010casov\u00e1 n\u00e1ro\u010dnost: 5-6 minut<\/p>\n<p>Jedn\u00e1 se o p\u0159\u00edklad z maturitn\u00edho testu.<\/p>\n","protected":false},"comment_status":"open","ping_status":"closed","template":"","class_list":["post-4749","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Obsah troj\u00faheln\u00edku - p\u0159\u00edklad | Studijni-svet.cz<\/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:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/obsah-trojuhelniku-priklad\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Obsah troj\u00faheln\u00edku - p\u0159\u00edklad | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed:&nbsp; Je d\u00e1n p\u011bti\u00faheln\u00edk ABCED kter\u00fd je slo\u017een ze \u010dtverce ABCD a troj\u00faheln\u00edku CED. V\u00edme obsahy \u010dtverce a troj\u00faheln\u00edku:$$\u0394 CED = 30 cm^{2}$$$$\u25a1 ABCD = 100 cm^{2}$$&nbsp; Jak\u00fd je obsah troj\u00faheln\u00edku ABE?A) Men\u0161\u00ed ne\u017e 75 cm\u00b2B) 75 cm\u00b2C) 78 cm\u00b2D) 80 cm\u00b2E) V\u011bt\u0161\u00ed ne\u017e 80 cm\u00b2 \u0158e\u0161en\u00ed: 1) Pomoc\u00ed vzore\u010dku na obsah \u010dtverce ABCD, vypo\u010d\u00edt\u00e1me ... 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