{"id":172235,"date":"2023-11-01T15:47:37","date_gmt":"2023-11-01T18:47:37","guid":{"rendered":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/?post_type=eaja&#038;p=172235"},"modified":"2024-03-29T18:47:56","modified_gmt":"2024-03-29T21:47:56","slug":"matematica-relacao-entre-o-numero-de-vertices-faces-e-arestas-dos-prismas","status":"publish","type":"eaja","link":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/eaja\/matematica-relacao-entre-o-numero-de-vertices-faces-e-arestas-dos-prismas\/","title":{"rendered":"Matem\u00e1tica &#8211; Rela\u00e7\u00e3o entre o n\u00famero de v\u00e9rtices, faces e arestas dos prismas"},"content":{"rendered":"\n<p class=\"has-text-align-center has-medium-font-size\"><strong>Esta proposta de atividade de Matem\u00e1tica \u00e9 destinada aos estudantes do 6\u00ba Per\u00edodo (8\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 has-custom-font-size has-small-font-size 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-medium-font-size\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/drive.google.com\/uc?export=douwnload&amp;id=1KUSpmcCHGGn95unJApM0YS_ImqVhQlyH\" target=\"_blank\" rel=\"noreferrer noopener\">BAIXE A ATIVIDADE<\/a><\/div>\n\n\n\n<div class=\"wp-block-button has-custom-font-size has-medium-font-size\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/drive.google.com\/uc?export=douwnload&amp;id=1Jwy_a9NyLLCpjdJ-KP1lpkXJpdijhZ-T\" target=\"_blank\" rel=\"noreferrer noopener\">BAIXE OS SLIDES<\/a><\/div>\n\n\n\n<div class=\"wp-block-button has-custom-font-size has-medium-font-size\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/drive.google.com\/uc?export=douwnload&amp;id=1SPgzWrp7fdRPbLsUjT-KPVFnoVai5S1e\" 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:21% auto\"><figure class=\"wp-block-media-text__media\"><img decoding=\"async\" width=\"144\" height=\"121\" src=\"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-content\/uploads\/2023\/11\/1-1.png\" alt=\"\" class=\"wp-image-172236 size-full\"\/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-text-color has-medium-font-size\" style=\"color:#1da22e\"><strong>Prisma<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Os <strong>prismas<\/strong> s\u00e3o figuras em 3D (tridimensionais) com <strong>duas bases<\/strong> iguais e paralelas, conectadas por <strong>faces retangulares<\/strong> ou paralelogramos.<\/p>\n\n\n\n<p class=\"has-small-font-size\">Imagem: canva.com\/prisma_<a href=\"https:\/\/encurtador.com.br\/hiY08\">https:\/\/encurtador.com.br\/hiY08<\/a><\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-medium-font-size\" style=\"color:#1da22e\"><strong>Alguns exemplos pr\u00e1ticos:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\"><strong>Caixa de sapatos<\/strong>: as bases s\u00e3o retangulares e as faces laterais s\u00e3o ret\u00e2ngulos.<\/li>\n\n\n\n<li class=\"has-medium-font-size\"><strong>L\u00e1pis sextavado<\/strong>: as bases s\u00e3o hex\u00e1gonos (6 lados) e as faces laterais s\u00e3o ret\u00e2ngulos.<\/li>\n\n\n\n<li class=\"has-medium-font-size\"><strong>Caixa de leite<\/strong>: as bases s\u00e3o retangulares e as faces laterais tamb\u00e9m s\u00e3o ret\u00e2ngulos.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/lh7-us.googleusercontent.com\/sftnifmfEKvofPyXLercNdEqlZyT-opDjzFnlsDkvwa2rhXec2C_4PlnajwMZcoorp9c3b2AbI2-6WsbHmukkF519uxEYuINpMjLVRzybKXhogpyBXScb83XD3Sbje61O-d0vERUKZgY\" alt=\"\" style=\"width:242px;height:96px\"\/><\/figure><\/div>\n\n\n<p class=\"has-text-align-center has-small-font-size\">Imagem: canva.com\/caixa_l\u00e1pis_leite_<a href=\"https:\/\/encurtador.com.br\/hiY08\">https:\/\/encurtador.com.br\/hiY08<\/a><\/p>\n\n\n\n<p class=\"has-text-color has-medium-font-size\" style=\"color:#1da22e\"><strong>Elementos de um prisma<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Al\u00e9m das faces laterais e das bases, os prismas possuem os seguintes elementos:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\"><strong>Arestas da base<\/strong>: s\u00e3o as arestas que formam o contorno da base do prisma.<\/li>\n\n\n\n<li class=\"has-medium-font-size\"><strong>Arestas laterais<\/strong>: s\u00e3o as arestas que conectam as arestas correspondentes das bases.<\/li>\n\n\n\n<li class=\"has-medium-font-size\"><strong>V\u00e9rtices<\/strong>: s\u00e3o os pontos onde as arestas se encontram.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/lh7-us.googleusercontent.com\/uo4lL0a087f5Ll_V5A6QF7mxdvah7LVFfzYLIKIaTFFpIEYjuiO_fFFgl68DZoVGjU4rDpLz_bD_Zbhl3GhSZ1OzLCpm9H7TT2OvRUhRZCHKhwuQ9Mj-ynB5qwy_TNb2oVDHADAguFww\" alt=\"\" style=\"width:153px;height:119px\"\/><\/figure><\/div>\n\n\n<p class=\"has-text-align-center has-small-font-size\">Imagem: canva.com\/prisma_<a href=\"https:\/\/encurtador.com.br\/hiY08\">https:\/\/encurtador.com.br\/hiY08<\/a><\/p>\n\n\n\n<p class=\"has-text-color has-medium-font-size\" style=\"color:#1da22e\"><strong>Como dar nome aos prismas?<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Os prismas s\u00e3o denominados de acordo com o <strong>tipo de pol\u00edgono<\/strong> que comp\u00f5e as suas <strong>bases<\/strong>.&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">P<strong>or exemplo:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-medium-font-size\"><strong>Prisma Retangular:<\/strong> possui bases retangulares.<\/li>\n\n\n\n<li class=\"has-medium-font-size\"><strong>Prisma Triangular:<\/strong> possui bases triangulares.<\/li>\n\n\n\n<li class=\"has-medium-font-size\"><strong>Prisma Pentagonal:<\/strong> possui bases pentagonais.<\/li>\n\n\n\n<li class=\"has-medium-font-size\"><strong>Prisma Hexagonal:<\/strong> possui bases hexagonais.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/lh7-us.googleusercontent.com\/UAEqKtZrccuQtg3yovWbP7pkhSZdgyjDC50ELfLo7HDXQbwhzrawSdRsE0ZrzDtFjO1HhjGwnvdLLoxLnBC4N9uzmCKMBwjm7dwhc7vXSUJdbcRmNqWcnEeYQtKQWojRgppC1oqXpmHP\" alt=\"\" style=\"width:269px;height:106px\"\/><\/figure><\/div>\n\n\n<p class=\"has-text-align-center has-small-font-size\">Imagem: canva.com\/prismas_<a href=\"https:\/\/encurtador.com.br\/hiY08\">https:\/\/encurtador.com.br\/hiY08<\/a><\/p>\n\n\n\n<p class=\"has-text-color has-medium-font-size\" style=\"color:#1da22e\"><strong>Rela\u00e7\u00e3o entre o n\u00famero de v\u00e9rtices, faces e arestas de um prisma<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">A rela\u00e7\u00e3o entre o n\u00famero de v\u00e9rtices (V), faces (F) e arestas (<em>A<\/em>) de um prisma \u00e9 dada pela <strong>F\u00f3rmula de Euler<\/strong>:<\/p>\n\n\n\n<p class=\"has-text-align-center has-vivid-red-color has-text-color has-medium-font-size\"><strong><em>V<\/em><\/strong><strong>+<\/strong><strong><em>F<\/em><\/strong><strong>\u2212<\/strong><strong><em>A<\/em><\/strong><strong>=2<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Esta f\u00f3rmula expressa a rela\u00e7\u00e3o caracter\u00edstica entre os v\u00e9rtices, as arestas e as faces de um prisma.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">Abaixo temos uma tabela onde poderemos verificar essa rela\u00e7\u00e3o.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" src=\"https:\/\/lh7-us.googleusercontent.com\/0wseBaymIPH3fjN7pUcC4ylefTqDpMs1QU9CqU_ZNaFTlSh16HzM2RYpoPBoCUNuA3rnFZ6S2tQNxq88TVPVOBQ_A3lGi4UIdr4waM6ZUmOlEmF5tCvNXH-DKyWMbqZy2ibwPnos27Yi\" alt=\"\" style=\"width:501px;height:170px\"\/><\/figure><\/div>\n\n\n<p class=\"has-medium-font-size\">Essa f\u00f3rmula \u00e9 \u00fatil para calcular o n\u00famero de v\u00e9rtices, arestas e faces de qualquer prisma, desde que se conhe\u00e7a os valores de dois desses elementos.<\/p>\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\"><strong>Atividade<\/strong><\/p>\n\n\n\n<p class=\"has-light-green-cyan-background-color has-background has-medium-font-size\"><strong>QUEST\u00c3O 01<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Determine:<br>A) O n\u00famero de faces de um prisma retangular.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">B) O n\u00famero de arestas de um prisma pentagonal.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">C) O n\u00famero de v\u00e9rtices de um prisma hexagonal.<\/p>\n\n\n\n<p class=\"has-light-green-cyan-background-color has-background has-medium-font-size\"><strong>QUEST\u00c3O 02<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">O n\u00famero de arestas de um prisma triangular \u00e9 igual a&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(A) 3&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(B) 6&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(C) 9&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(D) 12<\/p>\n\n\n\n<p class=\"has-light-green-cyan-background-color has-background has-medium-font-size\"><strong>QUEST\u00c3O 03<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Utilizando a rela\u00e7\u00e3o V+F-A=2, conhecida como a F\u00f3rmula de Euler para prismas, determinar:<\/p>\n\n\n\n<p class=\"has-medium-font-size\">A) O n\u00famero de faces de um prisma com 8 v\u00e9rtices e 12 arestas.&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">B) O n\u00famero de v\u00e9rtices de um prisma que possui 10 arestas e 7 faces.<\/p>\n\n\n\n<p class=\"has-light-green-cyan-background-color has-background has-medium-font-size\"><strong>QUEST\u00c3O 04<\/strong><\/p>\n\n\n\n<p class=\"has-medium-font-size\">O n\u00famero de v\u00e9rtices de um prisma com 10 arestas e 6 faces \u00e9 igual a&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(A) 8&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(B) 6&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(C) 10&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">(D) 12<\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td>Autoria<\/td><td>Professor 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 Desenvolvimento:<\/td><td>(EJAMA0622) Quantificar e estabelecer rela\u00e7\u00f5es entre o n\u00famero de v\u00e9rtices, faces e arestas de prismas e pir\u00e2mides, em fun\u00e7\u00e3o do pol\u00edgono da base.<\/td><\/tr><tr><td>Refer\u00eancias<\/td><td>SOUZA, Joamir Roberto de: Matem\u00e1tica realidade &amp; tecnologia: 9\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: 9\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 9\u00b0 ano: ensino fundamental, anos finais \/ Patricia Moreno Pataro, Rodrigo Balestri. &#8211; 1. ed. &#8211; S\u00e3o Paulo: Scipione, 2018.<br><\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"author":47,"featured_media":172236,"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":[100],"eaja_componente":[78],"class_list":["post-172235","eaja","type-eaja","status-publish","has-post-thumbnail","hentry","eaja_categoria-2o-segmento-7a-e-8a-serie","serie-8a-serie","eaja_componente-matematica","entry","has-media"],"acf":[],"_links":{"self":[{"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/eaja\/172235","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\/172236"}],"wp:attachment":[{"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/media?parent=172235"}],"wp:term":[{"taxonomy":"eaja_categoria","embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/eaja_categoria?post=172235"},{"taxonomy":"serie","embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/serie?post=172235"},{"taxonomy":"eaja_componente","embeddable":true,"href":"https:\/\/sme.goiania.go.gov.br\/conexaoescola\/wp-json\/wp\/v2\/eaja_componente?post=172235"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}