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A variety...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3433222/bcf9b315f4d8a7026da6b5c41f17b254/564x318_1"},"target":"_self","position":"3","reqid":"1766703548442404-2702035798366521080-balancer-l7leveler-kubr-yp-vla-151-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DhXQLZS8wCFw","linkTemplate":"/video/preview/9026240718931563047?parent-reqid=1766703548442404-2702035798366521080-balancer-l7leveler-kubr-yp-vla-151-BAL&text=Area+-+Topic&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Perimeter and Area Topic FOR Grade 5 Mathematics (Class 5)","related_orig_text":"Area - Topic","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Area - 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Üçgende Alan konusunun ayrıntılı ve yeni nesil sorularla konu anlatımı (İç Teğet Çember-Alan ilişkisi ve Ağırlık Merkezi-Alan ilişkisi) (Sayfa 73-74) *Pdf için aşağıdaki linke tıklayınız (Bölüm...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2407868/0459df1a78bd384916a9ad457b859671/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/q5FyLAEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"5","reqid":"1766703548442404-2702035798366521080-balancer-l7leveler-kubr-yp-vla-151-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1766703548442404-2702035798366521080-balancer-l7leveler-kubr-yp-vla-151-BAL&text=videoid:14316939886758145562","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeninin üçgende alan konusunu anlattığı eğitim içeriğidir. Öğretmen, çember-alan ilişkisi ve ağırlık merkezi alan ilişkisi gibi konuları detaylı şekilde açıklamaktadır.","Video, çember-alan ilişkisinin formülü (çevresi 2u ise alan = 2u × r) ile başlayıp, açıortayların kesim noktasının çemberin merkezi olduğu ve bu noktada açıortay kollarına çizilen dikmelerin çemberin yarıçapını verdiği ispatını sunmaktadır. Ardından ağırlık merkezi alan ilişkisi anlatılmakta ve üçgenlerin altı eşit parçaya ayrıldığı gösterilmektedir. İkinci bölümde ise analitik düzlemde dik koordinat düzlemi üzerinde üçgenlerin alanlarını hesaplama, ağırlık merkezinden paralel çizgilerle oluşan alanları bulma ve üçgenlerde kenar uzunluklarını hesaplama gibi sorular çözülmektedir.","Video, sayfa 74'ün çözümüyle sona ererken, bir sonraki videoda benzerlik ve alan ilişkisi konusunun anlatılacağı belirtilmektedir."]},"endTime":1062,"title":"Üçgende Alan ve Ağırlık Merkezi Konusu","beginTime":0}],"fullResult":[{"index":0,"title":"Çember-Alan İlişkisi","list":{"type":"unordered","items":["Üçgende alan konusunun devamında çember-alan ilişkisi ve ağırlık merkezi-alan ilişkisi anlatılacak.","Çemberin merkezi açıortayların kesim noktasıdır ve açıortayda kollara çizilen dikmeler birbirine eşittir.","Çemberin yarıçapı, açıortayda kollara çizilen dikmelerin uzunluğudur."]},"beginTime":9,"endTime":22,"href":"/video/preview/14316939886758145562?parent-reqid=1766703548442404-2702035798366521080-balancer-l7leveler-kubr-yp-vla-151-BAL&text=Area+-+Topic&t=9&ask_summarization=1"},{"index":1,"title":"Çember-Alan İlişkisinin İspatı","list":{"type":"unordered","items":["Çevresi u ise üçgen içerisinde alan formülü u çarpı r'dir, ancak bu formülü ezberlemek gerekmez.","Çemberin merkezi açıortayların kesim noktası olduğundan, açıortayda kollara çizilen dikmeler eşit olduğundan, yükseklere eşit olan üçgenlerin alanları tabanlarıyla doğru orantılıdır.","Çevreye iki dersek, üçgenlerin alanları a, 2a, 3a, 4a şeklinde olur ve toplam alan çevrenin yarısı çarpı yarıçap formülünü verir."]},"beginTime":22,"endTime":164,"href":"/video/preview/14316939886758145562?parent-reqid=1766703548442404-2702035798366521080-balancer-l7leveler-kubr-yp-vla-151-BAL&text=Area+-+Topic&t=22&ask_summarization=1"},{"index":2,"title":"Çember-Alan İlişkisi Örneği","list":{"type":"unordered","items":["9-12-15 üçgeni için açıortayların kesim noktası çemberin merkezidir ve dörtgenin alanı sorulmaktadır.","Üçgenin alanları tabanlarıyla doğru orantılı olduğundan, 9'daki alan 3a, 12'deki alan 4a, 15'teki alan 5a olarak hesaplanır.","Büyük dik üçgenin alanı dik kenarlar çarpımının yarısı olduğundan, 12a = 9×12/2 formülüyle a = 9/2 bulunur ve taralı alan 7×9/2 = 63/2 olarak hesaplanır."]},"beginTime":164,"endTime":275,"href":"/video/preview/14316939886758145562?parent-reqid=1766703548442404-2702035798366521080-balancer-l7leveler-kubr-yp-vla-151-BAL&text=Area+-+Topic&t=164&ask_summarization=1"},{"index":3,"title":"Dik Üçgen ve Çember Örneği","list":{"type":"unordered","items":["Bir dik üçgende dik kenar uzunluğu 6 birim, çemberin yarıçapı 2 birim olarak verilmiştir.","Çemberin merkezinden kenarlara çizilen dikmeler çemberin yarıçapını verir ve açıortay kollara çizilen dikmeler birbirine eşittir.","Pisagor bağıntısı kullanılarak dik üçgenin diğer kenarı 6 birim olarak bulunur ve alan 6×8/2 = 24 birim kare olarak hesaplanır."]},"beginTime":275,"endTime":426,"href":"/video/preview/14316939886758145562?parent-reqid=1766703548442404-2702035798366521080-balancer-l7leveler-kubr-yp-vla-151-BAL&text=Area+-+Topic&t=275&ask_summarization=1"},{"index":4,"title":"Ağırlık Merkezi-Alan İlişkisi","list":{"type":"unordered","items":["Üçgenin ağırlık merkezi olduğunda alan dağıtarak tüm parçaların eşit olduğunu görebiliriz.","Ağırlık merkezinden köşelere çizilen çizgiler üçgeni altı eşit parçaya böler.","Ağırlık merkezinden köşelere çizilen çizgilerle oluşan üçgenlerin alanları birbirine eşittir."]},"beginTime":426,"endTime":498,"href":"/video/preview/14316939886758145562?parent-reqid=1766703548442404-2702035798366521080-balancer-l7leveler-kubr-yp-vla-151-BAL&text=Area+-+Topic&t=426&ask_summarization=1"},{"index":5,"title":"Ağırlık Merkezi Örneği","list":{"type":"unordered","items":["ABC üçgeninin alanı 54 birim kare verilmiş ve taralı alan sorulmaktadır.","İki kenarortay varsa ağırlık merkezi bulunur ve üçüncü kenarortay çizildiğinde alanlar daha rahat dağıtılır.","Alan dağıtımı yapılarak taralı alan 345 birim kare olarak hesaplanır."]},"beginTime":498,"endTime":597,"href":"/video/preview/14316939886758145562?parent-reqid=1766703548442404-2702035798366521080-balancer-l7leveler-kubr-yp-vla-151-BAL&text=Area+-+Topic&t=498&ask_summarization=1"},{"index":6,"title":"Analitik Düzlemde Ağırlık Merkezi ve Alan Hesaplama","list":{"type":"unordered","items":["Analitik düzlemde dik koordinat düzlemi dik kestiği ve kenarortayların ağırlık merkezini oluşturduğu belirtiliyor.","Ağırlık merkezinden çizilen çizgiler üç eşit parçaya ayırır ve alan hesaplaması için bu özellik kullanılır.","Dik üçgenin alanı hesaplanarak, paralel alan 4 birim kare olarak bulunuyor."]},"beginTime":599,"endTime":673,"href":"/video/preview/14316939886758145562?parent-reqid=1766703548442404-2702035798366521080-balancer-l7leveler-kubr-yp-vla-151-BAL&text=Area+-+Topic&t=599&ask_summarization=1"},{"index":7,"title":"Ağırlık Merkezi ve Paralellik Özellikleri","list":{"type":"unordered","items":["Ağırlık merkezinden çizilen paraleller üç eşit parçaya ayırır ve bu özellik ispatlanabilir.","Ağırlık merkezinde oluşan üçgenlerin alanları birbirine eşittir.","Ağırlık merkezi ve paralellik özellikleri kullanılarak alan hesaplaması yapılabilir."]},"beginTime":673,"endTime":792,"href":"/video/preview/14316939886758145562?parent-reqid=1766703548442404-2702035798366521080-balancer-l7leveler-kubr-yp-vla-151-BAL&text=Area+-+Topic&t=673&ask_summarization=1"},{"index":8,"title":"Bahçe Problemi ve Ağırlık Merkezi","list":{"type":"unordered","items":["ABC üçgeni şeklindeki bir bahçede, ağırlık merkezinden kenarlara doğru hareket eden üç hareketli var.","Hareketlerin hızları eşit olduğundan, gittiği yollar dakikalarla doğru orantılıdır.","Ağırlık merkezinden kenarlara çizilen dikmelerin çarpımları birbirine eşittir ve bu özellik kullanılarak kenar uzunlukları hesaplanır."]},"beginTime":792,"endTime":1020,"href":"/video/preview/14316939886758145562?parent-reqid=1766703548442404-2702035798366521080-balancer-l7leveler-kubr-yp-vla-151-BAL&text=Area+-+Topic&t=792&ask_summarization=1"},{"index":9,"title":"Soru Çözümü ve Kapanış","list":{"type":"unordered","items":["Her bölümdeki son soruların daha seçici olduğu ve her tarz soruya alışkın olunması gerektiği vurgulanıyor.","Konu anlatımında kolay, orta ve zor soruların basamak basamak verildiği belirtiliyor.","Sayfa 75'te benzerlik alan ilişkisi konusu ele alınacak ve bir sonraki videoda anlatılacağı 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Trigonometri konusunda pratik yapmak isteyen öğrenciler için faydalı bir içerik sunulmaktadır."]},"endTime":1550,"title":"Geometri Kampı: Üçgenlerde Alan Hesaplama Yöntemleri","beginTime":0}],"fullResult":[{"index":0,"title":"Sinüs Alan Formülü","list":{"type":"unordered","items":["Bu video, geometri kampının altıncı haftasının ikinci videosu olup, alan bulma formüllerinden ikincisi olan sinüs alan formülünü ele alıyor.","Sinüs alan formülü, üçgende alan sorulduğunda kullanılır ve formülü b çarpı c çarpı sinüs alfa bölü iki şeklinde ifade edilir.","Üçgende 90 derece özel açı varsa, alan hesaplaması için tabana ait yükseklik kullanmak daha kolaydır."]},"beginTime":0,"endTime":96,"href":"/video/preview/10750300641315629926?parent-reqid=1766703548442404-2702035798366521080-balancer-l7leveler-kubr-yp-vla-151-BAL&text=Area+-+Topic&t=0&ask_summarization=1"},{"index":1,"title":"Sinüs Alan Formülünün Uygulanması","list":{"type":"unordered","items":["İlk örnekte, 30 derece, 6 derece ve 8 derece 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