{"id":170916,"date":"2023-10-06T16:00:00","date_gmt":"2023-10-06T19:00:00","guid":{"rendered":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/?post_type=eaja&#038;p=170916"},"modified":"2024-03-29T12:06:08","modified_gmt":"2024-03-29T15:06:08","slug":"matematica-angulos-internos-de-poligonos-regulares","status":"publish","type":"eaja","link":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/eaja\/matematica-angulos-internos-de-poligonos-regulares\/","title":{"rendered":"Matem\u00e1tica &#8211; \u00c2ngulos internos de pol\u00edgonos regulares"},"content":{"rendered":"\n<p class=\"has-text-align-center has-white-background-color has-background has-medium-font-size\"><strong>Esta proposta de atividade de&nbsp;MATEM\u00c1TICA&nbsp;\u00e9 destinada aos estudantes do 5\u00ba Per\u00edodo (7\u00aa s\u00e9rie)&nbsp;da Educa\u00e7\u00e3o de Jovens e Adultos \u2013 EJA<\/strong><\/p>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-16018d1d wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button has-custom-font-size has-small-font-size\"><a class=\"wp-block-button__link has-text-align-center wp-element-button\" href=\"https:\/\/drive.google.com\/uc?export=douwnload&amp;id=1ZvAGxIJVI7biCO9jJT3BzFPrlnzK9Wz7\" target=\"_blank\" rel=\"noreferrer noopener\">BAIXE A ATIVIDADE<\/a><\/div>\n\n\n\n<div class=\"wp-block-button has-custom-font-size has-small-font-size\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/drive.google.com\/uc?export=douwnload&amp;id=1CGbHdLwL7i6nVcbDipHaseej8OiKZoby\" target=\"_blank\" rel=\"noreferrer noopener\">BAIXE OS SLIDES<\/a><\/div>\n\n\n\n<div class=\"wp-block-button has-custom-font-size has-small-font-size\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/drive.google.com\/uc?export=douwnload&amp;id=1bySvvAfNFJEE8xujQpczIofHZt05VXV4\" target=\"_blank\" rel=\"noreferrer noopener\">BAIXE O TEXTO<\/a><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:34% auto\"><figure class=\"wp-block-media-text__media\"><img decoding=\"async\" width=\"258\" height=\"189\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2023\/10\/2.png\" alt=\"\" class=\"wp-image-170917 size-full\"\/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-text-color has-medium-font-size\" style=\"color:#1a12b5\"><strong>Uma breve revis\u00e3o de pol\u00edgonos<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Os <strong>pol\u00edgonos<\/strong> s\u00e3o figuras geom\u00e9tricas planas formadas por segmentos de reta chamados de <strong>lados<\/strong> que se encontram apenas em seus pontos finais (<strong>os<\/strong> <strong>v\u00e9rtices<\/strong>) e n\u00e3o se cruzam. Em cada v\u00e9rtice (ponto de encontro dos lados), s\u00e3o formados os <strong>\u00e2ngulos<\/strong>.<\/p>\n\n\n\n<p class=\"has-small-font-size\">Imagem: canva.com\/po\u00edgonos_regulares_<a href=\"https:\/\/l1nk.dev\/57dHO\">https:\/\/l1nk.dev\/57dHO<\/a><\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Por exemplo:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\"><strong>Tri\u00e2ngulo<\/strong>: pol\u00edgono de 3 lados, 3 v\u00e9rtices e 3 \u00e2ngulos.<\/li>\n\n\n\n<li class=\"has-medium-font-size\"><strong>Quadril\u00e1tero<\/strong>: pol\u00edgono de 4 lados, 4 v\u00e9rtices e 4 \u00e2ngulos.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-medium-font-size\" style=\"color:#1a12b5\"><strong>A soma dos \u00e2ngulos internos dos pol\u00edgonos<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">A soma dos \u00e2ngulos internos de um pol\u00edgono <strong>depende do n\u00famero de lados<\/strong> e pode ser calculada usando a seguinte f\u00f3rmula:<\/p>\n\n\n\n<p class=\"has-text-align-center has-vivid-red-color has-text-color has-medium-font-size\"><strong>S = (n-2).180\u00b0<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Onde <strong>S<\/strong> indica a soma dos \u00e2ngulos internos e <strong>n<\/strong> o n\u00famero de lados do pol\u00edgono.<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Por exemplo:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\">Tri\u00e2ngulos (3 lados):&nbsp; S = (3-2).180\u00b0 = 1.180\u00b0 = 180\u00b0<\/li>\n\n\n\n<li class=\"has-medium-font-size\">Quadril\u00e1teros (4 lados): S = (4-2).180\u00b0 = 2.180\u00b0 = 360\u00b0<\/li>\n\n\n\n<li class=\"has-medium-font-size\">Pent\u00e1gonos (5 lados): S = (5-2).180\u00b0 = 3.180\u00b0 = 540\u00b0<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-medium-font-size\" style=\"color:#1a12b5\"><strong>O que s\u00e3o pol\u00edgonos regulares?<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Os pol\u00edgonos regulares s\u00e3o figuras geom\u00e9tricas que possuem <strong>todos os lados e todos os \u00e2ngulos iguais<\/strong> (congruentes).<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Por exemplo:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\"><strong>Quadrado<\/strong>: possui os 4 lados com o mesmo comprimento e os 4 \u00e2ngulos congruentes (medidas iguais).<\/li>\n\n\n\n<li class=\"has-medium-font-size\"><strong>Tri\u00e2ngulo equil\u00e1tero<\/strong>: possui os 3 lados com o mesmo comprimento e os 3 \u00e2ngulos congruentes (medidas iguais).<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-medium-font-size\" style=\"color:#1a12b5\"><strong>Como determinar as medidas dos \u00e2ngulos internos (A<\/strong><strong><sub>i<\/sub><\/strong><strong>) de um pol\u00edgono regular?<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Basta seguir as etapas:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\">Determinar a soma dos \u00e2ngulos internos do pol\u00edgono;<\/li>\n\n\n\n<li class=\"has-medium-font-size\">Dividir o resultado desta soma pelo n\u00famero de lados desse pol\u00edgono.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Por exemplo:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\">Qual \u00e9 a medida de cada \u00e2ngulo interno de um hex\u00e1gono regular?<\/li>\n<\/ul>\n\n\n\n<p class=\"has-medium-font-size\">Como o hex\u00e1gono possui 6 lados, sua soma ser\u00e1 :<\/p>\n\n\n\n<p class=\"has-medium-font-size\">S=(n-2).180=(6-2).180\u00b0=4.180\u00b0=720\u00b0.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Dividindo esse resultado por 6 teremos: A<sub>i<\/sub> = 720\u00b0 : 6 = 120\u00b0<\/p>\n\n\n\n<p class=\"has-text-color has-medium-font-size\" style=\"color:#1a12b5\"><strong>Rela\u00e7\u00e3o entre a medida do \u00e2ngulo (A<\/strong><strong><sub>i<\/sub><\/strong><strong>) interno e externo (A<\/strong><strong><sub>e<\/sub><\/strong><strong>)<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Uma rela\u00e7\u00e3o bastante utilizada para determinar a medida do \u00e2ngulo externo de pol\u00edgono regular \u00e9 a seguinte:<\/p>\n\n\n\n<p class=\"has-text-align-center has-vivid-red-color has-text-color has-medium-font-size\"><strong>A medida do \u00e2ngulo externo de um pol\u00edgono regular \u00e9 igual a 180\u00b0 menos a medida do \u00e2ngulo interno.<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>Por exemplo:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\">Tri\u00e2ngulo equil\u00e1tero: A<sub>e<\/sub>=180\u00b0 &#8211; 60\u00b0 = 120\u00b0<\/li>\n\n\n\n<li class=\"has-medium-font-size\">Quadrado: A<sub>e<\/sub>=180\u00b0 &#8211; 90\u00b0 = 90\u00b0<\/li>\n\n\n\n<li class=\"has-medium-font-size\">Hex\u00e1gono regular: A<sub>e<\/sub>=180\u00b0 &#8211; 120\u00b0 = 60\u00b0<\/li>\n<\/ul>\n\n\n\n<p class=\"has-medium-font-size\">Ficamos por aqui, at\u00e9 o pr\u00f3ximo.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Atividade<\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background has-medium-font-size\"><strong>QUEST\u00c3O 01<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Sobre pol\u00edgonos regulares, podemos afirmar que eles<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(A) sempre possuem um n\u00famero \u00edmpar de lados.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(B) possuem lados de comprimentos diferentes.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(C) podem ter \u00e2ngulos agudos e obtusos.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(D) possuem todos os seus lados e \u00e2ngulos congruentes.<\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background has-medium-font-size\"><strong>QUEST\u00c3O 02<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Determinar a soma dos \u00e2ngulos internos dos seguintes pol\u00edgonos:<\/p>\n\n\n\n<p class=\"has-medium-font-size\">A) Hept\u00e1gono (pol\u00edgono com sete lados).<\/p>\n\n\n\n<p class=\"has-medium-font-size\">B) Oct\u00f3gono (pol\u00edgono com 8 lados).<\/p>\n\n\n\n<p class=\"has-medium-font-size\">C) Ene\u00e1gono (pol\u00edgono com 9 lados).<\/p>\n\n\n\n<p class=\"has-medium-font-size\">D) Dec\u00e1gono (pol\u00edgono com 10 lados).<\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background has-medium-font-size\"><strong>QUEST\u00c3O 03<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Determinar:<\/p>\n\n\n\n<p class=\"has-medium-font-size\">A) A medida do \u00e2ngulo interno de um hept\u00e1gono regular.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">B) O per\u00edmetro de um hept\u00e1gono regular com lado medindo 8 cent\u00edmetros de comprimento.<\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background has-medium-font-size\"><strong>QUEST\u00c3O 04<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Em rela\u00e7\u00e3o \u00e0 medida dos \u00e2ngulos internos de um tri\u00e2ngulo equil\u00e1tero e de um quadrado, podemos afirmar que<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(A) a medida dos \u00e2ngulos internos do tri\u00e2ngulo equil\u00e1tero \u00e9 igual a 70\u00b0.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(B) a medida dos \u00e2ngulos internos do quadrado \u00e9 igual a 60\u00b0.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(C) a medida dos \u00e2ngulos internos do tri\u00e2ngulo equil\u00e1tero \u00e9 igual a 60\u00b0 e do quadrado 85\u00b0.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(D) a medida dos \u00e2ngulos internos do tri\u00e2ngulo equil\u00e1tero \u00e9 igual a 60\u00b0 e do quadrado 90\u00b0.<\/p>\n\n\n\n<p class=\"has-white-color has-vivid-cyan-blue-background-color has-text-color has-background has-medium-font-size\"><strong>SAIBA MAIS<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Assista ao v\u00eddeo para aprender um pouco mais sobre pol\u00edgonos.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<p class=\"responsive-video-wrap clr\"><iframe title=\"Pol\u00edgonos\" width=\"1200\" height=\"675\" src=\"https:\/\/www.youtube.com\/embed\/pNNDj5u6Tas?start=379&#038;feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<\/div><figcaption class=\"wp-element-caption\">Canal do Prof. H\u00e9lio &lt;YouTube&gt;<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td>Autoria<\/td><td>Prof. H\u00e9lio Roberto da Rocha, Mestre em Matem\u00e1tica<\/td><\/tr><tr><td>Componente Curricular<\/td><td>Matem\u00e1tica<\/td><\/tr><tr><td>Objetivos de Aprendizagem e Conte\u00fados<\/td><td>(EJAMA0521) Calcular medidas de \u00e2ngulos internos de pol\u00edgonos regulares, e estabelecer rela\u00e7\u00f5es entre \u00e2ngulos internos e externos de pol\u00edgonos (tri\u00e2ngulo equil\u00e1tero e quadrado).<\/td><\/tr><tr><td>Refer\u00eancias<\/td><td>SOUZA, Joamir Roberto de: Matem\u00e1tica realidade &amp; tecnologia: 8\u00ba ano: ensino fundamental: anos finais \/ Joamir Roberto de Souza. \u2013 1. ed. \u2013 S\u00e3o Paulo: FTD, 2018.<br>GIOVANNI J\u00daNIOR, Jos\u00e9 Ruy &#8211; A conquista da matem\u00e1tica: 8\u00b0 ano: ensino fundamental: anos finais \/ Jos\u00e9 Ruy Giovanni J\u00fanior, Benedicto Castrucci. \u2014 4. ed. \u2014 S\u00e3o Paulo: FTD, 2018.<br>PATARO, Patricia Moreno Matem\u00e1tica essencial 8\u00b0 ano: ensino fundamental, anos finais \/ Patricia Moreno Pataro, Rodrigo Balestri. &#8211; 1. ed. &#8211; S\u00e3o Paulo: Scipione, 2018.<\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"author":47,"featured_media":170917,"template":"","meta":{"_acf_changed":false,"ocean_post_layout":"","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"","ocean_second_sidebar":"","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"","ocean_custom_header_template":"","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"","ocean_menu_typo_font_family":"","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":""},"eaja_categoria":[69],"serie":[76],"eaja_componente":[78],"class_list":["post-170916","eaja","type-eaja","status-publish","has-post-thumbnail","hentry","eaja_categoria-2o-segmento-7a-e-8a-serie","serie-7a-serie","eaja_componente-matematica","entry","has-media"],"acf":[],"_links":{"self":[{"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/eaja\/170916","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/eaja"}],"about":[{"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/types\/eaja"}],"author":[{"embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/users\/47"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/media\/170917"}],"wp:attachment":[{"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/media?parent=170916"}],"wp:term":[{"taxonomy":"eaja_categoria","embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/eaja_categoria?post=170916"},{"taxonomy":"serie","embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/serie?post=170916"},{"taxonomy":"eaja_componente","embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/eaja_componente?post=170916"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}