{"id":362,"date":"2022-12-28T12:02:12","date_gmt":"2022-12-28T12:02:12","guid":{"rendered":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/?page_id=362"},"modified":"2023-01-08T19:33:42","modified_gmt":"2023-01-08T19:33:42","slug":"prismen","status":"publish","type":"page","link":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/prismen\/","title":{"rendered":"Prismen"},"content":{"rendered":"\n<p>Was ist ein Prisma? Du kannst es an folgenden Eigenschaften erkennen:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Grund- und Deckfl\u00e4che sind deckungsgleich (identisch)<\/li>\n\n\n\n<li>Grund- und Deckfl\u00e4che bestehen aus einem beliebigen Vieleck (z.B. Dreieck, Viereck, Achteck&#8230;)<\/li>\n\n\n\n<li>Die Seitenkanten sind parallel zueinander und gleich lang<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Beispiele<\/h2>\n\n\n<style>#kt-layout-id_671dce-4b > .kt-row-column-wrap{align-content:start;}:where(#kt-layout-id_671dce-4b > .kt-row-column-wrap) > .wp-block-kadence-column{justify-content:start;}#kt-layout-id_671dce-4b > .kt-row-column-wrap{column-gap:var(--global-kb-gap-md, 2rem);row-gap:var(--global-kb-gap-md, 2rem);padding-top:var( --global-kb-row-default-top, 25px );padding-bottom:var( --global-kb-row-default-bottom, 25px );padding-top:0px;padding-bottom:17px;}#kt-layout-id_671dce-4b > .kt-row-column-wrap > div:not(.added-for-specificity){grid-column:initial;}#kt-layout-id_671dce-4b > .kt-row-column-wrap{grid-template-columns:repeat(4, minmax(0, 1fr));}#kt-layout-id_671dce-4b > .kt-row-layout-overlay{opacity:0.30;}@media all and (max-width: 1024px){#kt-layout-id_671dce-4b > .kt-row-column-wrap > div:not(.added-for-specificity){grid-column:initial;}}@media all and (max-width: 1024px){#kt-layout-id_671dce-4b > .kt-row-column-wrap{grid-template-columns:repeat(4, minmax(0, 1fr));}}@media all and (max-width: 767px){#kt-layout-id_671dce-4b > .kt-row-column-wrap > div:not(.added-for-specificity){grid-column:initial;}#kt-layout-id_671dce-4b > .kt-row-column-wrap{grid-template-columns:minmax(0, 1fr);}}<\/style>\n<div class=\"wp-block-kadence-rowlayout alignnone\"><div id=\"kt-layout-id_671dce-4b\" class=\"kt-row-layout-inner kt-layout-id_671dce-4b\"><div class=\"kt-row-column-wrap kt-has-4-columns kt-gutter-default kt-v-gutter-default kt-row-valign-top kt-row-layout-equal kt-tab-layout-inherit kt-m-colapse-left-to-right kt-mobile-layout-row\"><style>.kadence-column_9396f5-c8 > .kt-inside-inner-col{border-top-width:0px;border-right-width:0px;border-bottom-width:0px;border-left-width:0px;}.kadence-column_9396f5-c8 > .kt-inside-inner-col,.kadence-column_9396f5-c8 > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column_9396f5-c8 > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column_9396f5-c8 > .kt-inside-inner-col{flex-direction:column;}.kadence-column_9396f5-c8 > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column_9396f5-c8 > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column_9396f5-c8{position:relative;}@media all and (max-width: 1024px){.kadence-column_9396f5-c8 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column_9396f5-c8 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\n<div class=\"wp-block-kadence-column inner-column-1 kadence-column_9396f5-c8\"><div class=\"kt-inside-inner-col\">\n<p class=\"has-text-align-center\"><strong>Dreiecksprisma<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"842\" height=\"636\" src=\"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/dreiecksprisma.jpg\" alt=\"\" class=\"wp-image-527\" srcset=\"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/dreiecksprisma.jpg 842w, https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/dreiecksprisma-300x227.jpg 300w, https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/dreiecksprisma-768x580.jpg 768w\" sizes=\"auto, (max-width: 842px) 100vw, 842px\" \/><\/figure>\n<\/div><\/div>\n\n\n<style>.kadence-column_22faaa-ee > .kt-inside-inner-col{border-top-width:0px;border-right-width:0px;border-bottom-width:0px;border-left-width:0px;}.kadence-column_22faaa-ee > .kt-inside-inner-col,.kadence-column_22faaa-ee > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column_22faaa-ee > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column_22faaa-ee > .kt-inside-inner-col{flex-direction:column;}.kadence-column_22faaa-ee > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column_22faaa-ee > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column_22faaa-ee{position:relative;}@media all and (max-width: 1024px){.kadence-column_22faaa-ee > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column_22faaa-ee > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\n<div class=\"wp-block-kadence-column inner-column-2 kadence-column_22faaa-ee\"><div class=\"kt-inside-inner-col\">\n<p class=\"has-text-align-center\"><strong>Quader<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"770\" height=\"661\" src=\"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/image-2.png\" alt=\"\" class=\"wp-image-524\" srcset=\"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/image-2.png 770w, https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/image-2-300x258.png 300w, https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/image-2-768x659.png 768w\" sizes=\"auto, (max-width: 770px) 100vw, 770px\" \/><\/figure>\n<\/div><\/div>\n\n\n<style>.kadence-column_75d540-29 > .kt-inside-inner-col{border-top-width:0px;border-right-width:0px;border-bottom-width:0px;border-left-width:0px;}.kadence-column_75d540-29 > .kt-inside-inner-col,.kadence-column_75d540-29 > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column_75d540-29 > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column_75d540-29 > .kt-inside-inner-col{flex-direction:column;}.kadence-column_75d540-29 > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column_75d540-29 > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column_75d540-29{position:relative;}@media all and (max-width: 1024px){.kadence-column_75d540-29 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column_75d540-29 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\n<div class=\"wp-block-kadence-column inner-column-3 kadence-column_75d540-29\"><div class=\"kt-inside-inner-col\">\n<p class=\"has-text-align-center\"><strong>Trapezprisma<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-medium\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"161\" src=\"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/trapezprisma-300x161.jpg\" alt=\"\" class=\"wp-image-529\" srcset=\"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/trapezprisma-300x161.jpg 300w, https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/trapezprisma-1024x550.jpg 1024w, https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/trapezprisma-768x412.jpg 768w, https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/trapezprisma.jpg 1186w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n<\/div><\/div>\n\n\n<style>.kadence-column_fe7045-73 > .kt-inside-inner-col{border-top-width:0px;border-right-width:0px;border-bottom-width:0px;border-left-width:0px;}.kadence-column_fe7045-73 > .kt-inside-inner-col,.kadence-column_fe7045-73 > .kt-inside-inner-col:before{border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;}.kadence-column_fe7045-73 > .kt-inside-inner-col{column-gap:var(--global-kb-gap-sm, 1rem);}.kadence-column_fe7045-73 > .kt-inside-inner-col{flex-direction:column;}.kadence-column_fe7045-73 > .kt-inside-inner-col > .aligncenter{width:100%;}.kadence-column_fe7045-73 > .kt-inside-inner-col:before{opacity:0.3;}.kadence-column_fe7045-73{position:relative;}@media all and (max-width: 1024px){.kadence-column_fe7045-73 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}@media all and (max-width: 767px){.kadence-column_fe7045-73 > .kt-inside-inner-col{flex-direction:column;justify-content:center;}}<\/style>\n<div class=\"wp-block-kadence-column inner-column-4 kadence-column_fe7045-73\"><div class=\"kt-inside-inner-col\">\n<p class=\"has-text-align-center\"><strong>W\u00fcrfel<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"420\" height=\"417\" src=\"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/Screenshot-2023-01-08-190535.jpg\" alt=\"\" class=\"wp-image-532\" srcset=\"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/Screenshot-2023-01-08-190535.jpg 420w, https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/Screenshot-2023-01-08-190535-300x298.jpg 300w, https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/Screenshot-2023-01-08-190535-150x150.jpg 150w\" sizes=\"auto, (max-width: 420px) 100vw, 420px\" \/><\/figure>\n<\/div><\/div>\n<\/div><\/div><\/div>\n\n\n\n<p><strong>Berechnung von Mantelfl\u00e4che M, Oberfl\u00e4che O und Volumen V eines Prismas<\/strong><\/p>\n\n\n\n<p><strong>Beispielaufgabe:<\/strong> Vom gegebenen Dreiecksprisma sollen die Mantelfl\u00e4che, die Oberfl\u00e4che und das Volumen berechnet werden. Informiere dich im nachfolgenden Text und berechne selbst. Viel Erfolg \ud83d\ude42<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/dreiecksprisma-mit-werten-1.jpg\" alt=\"\" class=\"wp-image-537\" width=\"624\" height=\"388\" srcset=\"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/dreiecksprisma-mit-werten-1.jpg 832w, https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/dreiecksprisma-mit-werten-1-300x186.jpg 300w, https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-content\/uploads\/2023\/01\/dreiecksprisma-mit-werten-1-768x477.jpg 768w\" sizes=\"auto, (max-width: 624px) 100vw, 624px\" \/><\/figure>\n\n\n<style>.kt-accordion-id_2e6970-82 .kt-accordion-inner-wrap{column-gap:var(--global-kb-gap-md, 2rem);row-gap:0px;}.kt-accordion-id_2e6970-82 .kt-accordion-panel-inner{border-top-width:0px;border-right-width:0px;border-bottom-width:0px;border-left-width:0px;padding-top:var(--global-kb-spacing-sm, 1.5rem);padding-right:var(--global-kb-spacing-sm, 1.5rem);padding-bottom:var(--global-kb-spacing-sm, 1.5rem);padding-left:var(--global-kb-spacing-sm, 1.5rem);}.kt-accordion-id_2e6970-82 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header{border-top-color:#555555;border-right-color:#555555;border-bottom-color:#555555;border-left-color:#555555;border-top-width:0px;border-right-width:0px;border-bottom-width:0px;border-left-width:0px;border-top-left-radius:0px;border-top-right-radius:0px;border-bottom-right-radius:0px;border-bottom-left-radius:0px;background:#f2f2f2;font-size:18px;line-height:24px;color:#555555;padding-top:10px;padding-right:14px;padding-bottom:10px;padding-left:14px;}.kt-accordion-id_2e6970-82:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id_2e6970-82:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap .kt-blocks-accordion-icon-trigger:before{background:#555555;}.kt-accordion-id_2e6970-82:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger{background:#555555;}.kt-accordion-id_2e6970-82:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id_2e6970-82:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-icon-trigger:before{background:#f2f2f2;}.kt-accordion-id_2e6970-82 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header:hover, \n\t\t\t\tbody:not(.hide-focus-outline) .kt-accordion-id_2e6970-82 .kt-blocks-accordion-header:focus-visible{color:#444444;background:#eeeeee;border-top-color:#eeeeee;border-right-color:#eeeeee;border-bottom-color:#eeeeee;border-left-color:#eeeeee;}.kt-accordion-id_2e6970-82:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id_2e6970-82:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id_2e6970-82:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion--visible .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id_2e6970-82:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger:before{background:#444444;}.kt-accordion-id_2e6970-82:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger, body:not(.hide-focus-outline) .kt-accordion-id_2e6970-82:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger{background:#444444;}.kt-accordion-id_2e6970-82:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id_2e6970-82:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before, body:not(.hide-focus-outline) .kt-accordion-id_2e6970-82:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger:after, body:not(.hide-focus-outline) .kt-accordion-id_2e6970-82:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible .kt-blocks-accordion-icon-trigger:before{background:#eeeeee;}.kt-accordion-id_2e6970-82 .kt-accordion-header-wrap .kt-blocks-accordion-header:focus-visible,\n\t\t\t\t.kt-accordion-id_2e6970-82 > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active{color:#ffffff;background:#444444;border-top-color:#444444;border-right-color:#444444;border-bottom-color:#444444;border-left-color:#444444;}.kt-accordion-id_2e6970-82:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id_2e6970-82:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle )  > .kt-accordion-inner-wrap > .wp-block-kadence-pane > .kt-accordion-header-wrap > .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#ffffff;}.kt-accordion-id_2e6970-82:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger{background:#ffffff;}.kt-accordion-id_2e6970-82:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id_2e6970-82:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before{background:#444444;}@media all and (max-width: 767px){.kt-accordion-id_2e6970-82 .kt-accordion-inner-wrap{display:block;}.kt-accordion-id_2e6970-82 .kt-accordion-inner-wrap .kt-accordion-pane:not(:first-child){margin-top:0px;}}<\/style>\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-wrap kt-accordion-id_2e6970-82 kt-accordion-has-4-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-basic kt-accodion-icon-side-right\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"0\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane_f17bf8-7d\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">Informationstext Mantelfl\u00e4che, Oberfl\u00e4che und Volumen eines Prismas<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p>Bevor wir mit der Berechnung in einem Prisma beginnen, m\u00fcssen wir immer \u00fcberlegen, wo sich die deckungsgleichen Deck-bzw. Grundfl\u00e4chen befinden. Im hier abgebildeten Dreiecksprisma sind das die beiden blau markierten Dreiecke! Sie sind kongruent (das bedeutet deckungsgleich, also absolut identisch) und liegen sich parallel gegen\u00fcber.<\/p>\n\n\n\n<p>Die <strong>Mantelfl\u00e4che M<\/strong> ist der komplette Fl\u00e4cheninhalt der Seitenfl\u00e4chen (ohne Grund- und Deckfl\u00e4che). Nat\u00fcrlich k\u00f6nntest du diese (hier 3) Fl\u00e4chen einzeln berechne und addieren, es geht aber bei jedem Prisma auch so:<\/p>\n\n\n\n<p><strong>Mantelfl\u00e4che M = Umfang der Grundfl\u00e4che * H\u00f6he des Prismas.<\/strong><\/p>\n\n\n\n<p><strong>M = U*h<\/strong><\/p>\n\n\n\n<p>Die <strong>Oberfl\u00e4che O <\/strong>eines jeden Prismas berechnet sich als <strong>2* Grundfl\u00e4che + Mantelfl\u00e4che<\/strong><\/p>\n\n\n\n<p><strong>O = 2*G + M<\/strong><\/p>\n\n\n\n<p>Das Volumen eines <strong>jeden <\/strong>Prismas berechnet sich als Volumen = Grundfl\u00e4che * H\u00f6he des Prismas<\/p>\n\n\n\n<p><strong>V = G*h<\/strong><\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-2 kt-pane_3a99e0-e6\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">L\u00f6sung Beispielaufgabe<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p><strong>Mantelfl\u00e4che M = Umfang * H\u00f6he des Prismas.<\/strong><\/p>\n\n\n\n<p>Umfang = 4 + 2,83 + 2,83 = 9,66<\/p>\n\n\n\n<p>H\u00f6he des Prismas = 3,61 (Achtung: nicht mit der H\u00f6he des Dreiecks verwechseln!)<\/p>\n\n\n\n<p>M = 9,66 * 3,61 = <strong>34,8728 LE\u00b2<\/strong><\/p>\n\n\n\n<p><strong>Oberfl\u00e4che = 2*G + M<\/strong><\/p>\n\n\n\n<p>Die Grundfl\u00e4che ist hier ein Dreieck. Der Fl\u00e4cheninhalt l\u00e4sst sich wie folgt bestimmen:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>A_{Dreieck}=\\frac{g*h}{2}=\\frac{4*2}{2}=4<\/pre><\/div>\n\n\n\n<p>Die Oberfl\u00e4che des Prismas betr\u00e4gt dementsprechend: <strong>O = 2*4 + 34,8728 = 42,8728 L<\/strong><\/p>\n\n\n\n<p><strong>Volumen<\/strong> <strong>V = G*h<\/strong><\/p>\n\n\n\n<p>Die Grundfl\u00e4che ist weiterhin ein Dreieck mit einem Fl\u00e4cheninhalt von 4 LE\u00b2<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>V = G*h_{Prisma}=4*3,61=14,44\\ LE\u00b3<\/pre><\/div>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-3 kt-pane_a0ad6e-57\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">Lernvideos Eigenschaften und Berechnungen am Prisma<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<h2 class=\"wp-block-heading\"><strong>Eigenschaften eines Prismas<\/strong><\/h2>\n\n\n\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-9\" class=\"h5p-iframe\" data-content-id=\"9\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"01 Prisma (Eigenschaften, Oberfl\u00e4che, Volumen)\"><\/iframe><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Berechnungen am Prisma<\/strong><\/h2>\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<iframe loading=\"lazy\" hcb-fetch-image-from=\"https:\/\/youtu.be\/0HQU3s_i6ws\" title=\"Volumen, Oberfl\u00e4che, Mantelfl\u00e4che eines Prismas\" width=\"800\" height=\"450\" src=\"https:\/\/www.youtube.com\/embed\/0HQU3s_i6ws?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-4 kt-pane_cc714a-96\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">Digitale \u00dcbungsaufgaben<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p>Der <a href=\"https:\/\/mathe.aufgabenfuchs.de\/koerper\/prisma.shtml\">Aufgabenfuchs<\/a> bietet hier tolle \u00dcbungsaufgaben.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/mathe.aufgabenfuchs.de\/koerper\/prisma.shtml\">\u00dcbungsaufgaben Prisma<\/a><\/div>\n<\/div>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Was ist ein Prisma? Du kannst es an folgenden Eigenschaften erkennen: Beispiele Dreiecksprisma Quader Trapezprisma W\u00fcrfel Berechnung von Mantelfl\u00e4che M,<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"colormag_page_container_layout":"default_layout","colormag_page_sidebar_layout":"default_layout","footnotes":""},"class_list":["post-362","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/pages\/362","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/comments?post=362"}],"version-history":[{"count":16,"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/pages\/362\/revisions"}],"predecessor-version":[{"id":550,"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/pages\/362\/revisions\/550"}],"wp:attachment":[{"href":"https:\/\/nachhilfe-wirtschaftsschule.de\/wordpress\/wp-json\/wp\/v2\/media?parent=362"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}