{"id":4747,"date":"2022-09-01T15:03:09","date_gmt":"2022-09-01T13:03:09","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/obsah-mnohouohelniku-priklad-1\/"},"modified":"2022-09-01T15:03:09","modified_gmt":"2022-09-01T13:03:09","slug":"obsah-mnohouohelniku-priklad-1","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/obsah-mnohouohelniku-priklad-1\/","title":{"rendered":"Obsah mnoho\u00faoheln\u00edku – p\u0159\u00edklad 1"},"content":{"rendered":"

Zad\u00e1n\u00ed:<\/strong> Osov\u011b soum\u011brn\u00fd rovinn\u00fd obrazec je tvo\u0159en ze 2 shodn\u00fdch koso\u010dtverc\u016f. Obvod obrazce je 24 cm a je vyzna\u010den\u00fd \u00fahel \u03c6<\/strong> m\u00e1 velikost 140\u00b0<\/strong>.<\/p>\n

\"\"<\/p>\n

Jak\u00fd je obsah obrazce?<\/strong>
(V\u00fdsledek je zaokrouhlen na cel\u00e9 cm \u010dtvere\u010dn\u00ed<\/strong>)
$$a) 21 cm^{2}$$
$$b) 24 cm^{2}$$
$$c) 27 cm^{2}$$
$$d) 28 cm^{2}$$
$$e) 30 cm^{2}$$<\/p>\n

\u0158e\u0161en\u00ed:<\/strong><\/p>\n

Obrazec je osov\u011b soum\u011brn\u00fd obrazec a lze jej rozd\u011blit na dva toto\u017en\u00e9 koso\u010dtverce. Jejich vnit\u0159n\u00ed \u00fahly jsou vyzna\u010deny na obr\u00e1zku.
1) Pro v\u00fdpo\u010det obsahu poloviny obrazce vyu\u017eijeme n\u00e1sleduj\u00edc\u00ed vzorec
$$s_{k} = a^{2} \u00b7 sin \u03b1$$
2) Do vzorce dosad\u00edme
$$s_{k} = 4^{2} \u00b7 sin 20\u00b0$$
3) Vypo\u010d\u00edt\u00e1me
$$ s_{k} = 14,6 cm^{2}$$
4) Nyn\u00ed pot\u0159ebujeme vypo\u010d\u00edtat obsah cel\u00e9ho obrazce
$$s_{o} = 2 \u00b7 s_{k}$$
5) Dosad\u00edme
$$s_{o} = 2 \u00b7 15$$
6) Vyjde n\u00e1m spr\u00e1vn\u00e1 odpov\u011b\u010f za (e)<\/strong>
$$s_{o} = 30 cm^{2}$$<\/p>\n

\u010casov\u00e1 n\u00e1ro\u010dnost: 5-6 minut<\/p>\n

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-4747","lesson","type-lesson","status-publish","hentry"],"yoast_head":"\nObsah mnoho\u00faoheln\u00edku - p\u0159\u00edklad 1 | 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-mnohouohelniku-priklad-1\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Obsah mnoho\u00faoheln\u00edku - p\u0159\u00edklad 1 | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: Osov\u011b soum\u011brn\u00fd rovinn\u00fd obrazec je tvo\u0159en ze 2 shodn\u00fdch koso\u010dtverc\u016f. 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