{"id":55690,"date":"2025-10-10T08:50:04","date_gmt":"2025-10-10T07:50:04","guid":{"rendered":"https:\/\/studybuddy.se\/?p=55690"},"modified":"2026-10-16T09:51:25","modified_gmt":"2026-10-16T08:51:25","slug":"area","status":"publish","type":"post","link":"https:\/\/studybuddy.se\/en\/area\/","title":{"rendered":"Area – R\u00e4kna ut arean av geometriska figurer"},"content":{"rendered":"

Vad \u00e4r area?<\/strong> Area \u00e4r ett m\u00e5tt p\u00e5 hur stor en yta \u00e4r. Inom geometrin anv\u00e4nder vi area f\u00f6r att beskriva storleken p\u00e5 tv\u00e5dimensionella figurer, till exempel hur stor ytan av en rektangel eller cirkel \u00e4r. Arean m\u00e4ts i kvadratenheter<\/strong>, vilket betyder att man anger arean i rutor av en viss l\u00e4ngd. Vanliga enheter f\u00f6r area \u00e4r till exempel kvadratcentimeter (cm\u00b2) och kvadratmeter (m\u00b2). Om en kvadrat har sidan 1 cm, s\u00e4ger vi att dess area \u00e4r 1 kvadratcentimeter, skrivet som 1 cm\u00b2. Area handlar allts\u00e5 om ytan inuti en figur, inte om str\u00e4ckan runt omkring (den str\u00e4ckan kallas omkrets<\/strong>).<\/p>\n

Hur ber\u00e4knar man area?<\/strong> F\u00f6r att ber\u00e4kna area av en figur kan man t\u00e4nka sig att man t\u00e4cker figuren med sm\u00e5 enhetsrutor och sedan r\u00e4knar alla rutor. I praktiken anv\u00e4nder vi dock f\u00e4rdiga formler f\u00f6r olika former ist\u00e4llet f\u00f6r att rita upp rutor varje g\u00e5ng. Vilken formel man anv\u00e4nder beror p\u00e5 vilken form figuren har. Nedan g\u00e5r vi igenom hur man r\u00e4knar ut arean f\u00f6r n\u00e5gra vanliga geometriska figurer: rektangel, kvadrat, triangel, cirkel<\/strong> (samt parallellogram och trapets f\u00f6r den som \u00e4r nyfiken). Vi visar ocks\u00e5 exempel p\u00e5 hur area anv\u00e4nds i verkliga livet.<\/p>\n

Rektangelns area<\/h2>\n

En rektangel \u00e4r en fyrh\u00f6rning d\u00e4r motst\u00e5ende sidor \u00e4r parallella och varje h\u00f6rn \u00e4r 90\u00b0. F\u00f6r att r\u00e4kna ut arean av en rektangel multiplicerar man rektangelns l\u00e4ngd med dess bredd. Man kan ocks\u00e5 kalla l\u00e4ngden f\u00f6r bas (b) och bredden f\u00f6r h\u00f6jd (h) i detta sammanhang. Formeln f\u00f6r rektangelns area \u00e4r allts\u00e5:<\/p>\n

Area = l\u00e4ngd \u00d7 bredd<\/strong><\/p>\n

\"R\u00e4kna<\/p>\n

Om till exempel en rektangel har l\u00e4ngden 6 cm och bredden 3 cm, blir arean 6 \u00d7 3 = 18
\n6\u00d73=18 kvadratcentimeter (18 cm\u00b2). Det spelar ingen roll om rektangeln \u00e4r l\u00e5ng och smal eller mer kvadratisk \u2013 s\u00e5 l\u00e4nge du multiplicerar en sidol\u00e4ngd med den andra f\u00e5r du ytan.<\/p>\n

Kvadratens area<\/h2>\n

En kvadrat \u00e4r en specialfall av rektangeln d\u00e4r alla sidor \u00e4r lika l\u00e5nga. Att ber\u00e4kna arean av en kvadrat \u00e4r d\u00e4rf\u00f6r extra enkelt: man multiplicerar sidan med sig sj\u00e4lv. Formeln kan skrivas som:<\/p>\n

Area = sida \u00d7 sida<\/strong><\/p>\n

\"ber\u00e4kna<\/p>\n

Om en kvadrat har sidl\u00e4ngden 5 m, blir arean 5 \u00d7 5 = 25
\n5\u00d75=25 kvadratmeter (25 m\u00b2). Ibland s\u00e4ger man ”sidl\u00e4ngden i kvadrat” f\u00f6r att beskriva detta (d\u00e4rav ordet kvadratcentimeter f\u00f6r en liten ruts area). Precis som med rektangeln kommer en st\u00f6rre sidl\u00e4ngd ge st\u00f6rre area.<\/p>\n

Triangelns area<\/h2>\n

En triangel \u00e4r en figur med tre sidor. Arean av en triangel ber\u00e4knas med basen och h\u00f6jden, precis som f\u00f6r en rektangel, men eftersom triangeln bara t\u00e4cker halva den rektangel som har samma bas och h\u00f6jd m\u00e5ste vi dela med 2. Formeln f\u00f6r att r\u00e4kna ut arean av en triangel \u00e4r:<\/p>\n

Area<\/strong> = (b \u00d7 h) \/ 2<\/strong><\/p>\n

\"ber\u00e4kna\"area<\/p>\n

Basen (b) \u00e4r ofta en triangelns nedersta sida, och h\u00f6jden (h) \u00e4r avst\u00e5ndet fr\u00e5n basen rakt upp till triangelns spets (dvs. en linje vinkelr\u00e4tt mot basen). H\u00f6jden beh\u00f6ver inte vara en av triangelns egna sidor, utan kan vara en linje inuti triangeln om den \u00e4r spetsig eller trubbig. Till exempel, om en triangel har basen 8 dm och h\u00f6jden 5 dm, blir arean (8 \u00d7 5) \/ 2 = 20 kvadratdecimeter (20 dm\u00b2).<\/p>\n

Notera:<\/strong> Formeln ovan fungerar f\u00f6r alla trianglar, oavsett form (r\u00e4tvinklig, likbent, osv), s\u00e5 l\u00e4nge man k\u00e4nner till en bas och den tillh\u00f6rande h\u00f6jden. Om triangeln \u00e4r r\u00e4tvinklig (har en 90\u00b0 vinkel) kan de tv\u00e5 benen vid den r\u00e4ta vinkeln tas som bas och h\u00f6jd direkt.<\/p>\n

Cirkelns area<\/h2>\n

En cirkel \u00e4r en rund figur, och dess area ber\u00e4knas annorlunda \u00e4n fyrh\u00f6rningar och trianglar. F\u00f6r att r\u00e4kna ut arean av en cirkel beh\u00f6ver man k\u00e4nna till cirkelns radie. Radien (r) \u00e4r avst\u00e5ndet fr\u00e5n mittpunkten till cirkelns kant. (Diametern \u00e4r hela cirkelns bredd rakt \u00f6ver genom mittpunkten, och diametern \u00e4r dubbelt s\u00e5 l\u00e5ng som radien.) Formeln f\u00f6r cirkelns area \u00e4r:<\/p>\n

Area = \u03c0 \u00d7 r\u00b2<\/strong><\/p>\n

\"ber\u00e4kna<\/p>\n

H\u00e4r \u00e4r \u03c0 (pi) en matematisk konstant som \u00e4r ungef\u00e4r 3,14. Uttrycket \ud835\udc5f\u00b2 betyder ”r g\u00e5nger r” (allts\u00e5 radien multiplicerat med sig sj\u00e4lv). Om en cirkel har radien 10 cm blir arean ungef\u00e4r 3,14\u00d710\u00b2 = 3,14\u00d7100 = 314 kvadratcentimeter (314 cm\u00b2). Vi avrundar oftast v\u00e4rdet eftersom \u03c0 har o\u00e4ndligt m\u00e5nga decimaler.<\/p>\n

Om du vill l\u00e4sa mer om hur man ber\u00e4knar omkretsen av en cirkel, se v\u00e5r guide om omkrets av cirkel<\/a>.<\/p>\n

Parallellogrammens area<\/h2>\n

En parallellogram \u00e4r en fyrh\u00f6rning d\u00e4r motst\u00e5ende sidor \u00e4r parallella (en lutad rektangel kan man s\u00e4ga). F\u00f6r att ber\u00e4kna arean av en parallellogram multiplicerar man basen med h\u00f6jden, precis som hos en rektangel. Skillnaden \u00e4r att h\u00f6jden h\u00e4r \u00e4r det vinkelr\u00e4ta avst\u00e5ndet mellan de parallella baserna (allts\u00e5 ”lodr\u00e4ta” h\u00f6jden, inte l\u00e4ngden av den lutande sidan). Formeln \u00e4r:<\/p>\n

Area = bas \u00d7 h\u00f6jd<\/strong><\/p>\n

\"Ber\u00e4kna<\/p>\n

Du kan t\u00e4nka dig att en parallellogram med basen b och h\u00f6jden h kan ”skjutas ihop” till en rektangel med samma m\u00e5tt utan att arean \u00e4ndras. D\u00e4rf\u00f6r \u00e4r formeln likadan.<\/p>\n

Trapetsens area<\/h2>\n

En trapets (eller parallelltrapets) \u00e4r en fyrh\u00f6rning d\u00e4r tv\u00e5 sidor \u00e4r parallella men de andra tv\u00e5 inte \u00e4r det. De parallella sidorna kallas ofta baser i detta sammanhang. F\u00f6r att ber\u00e4kna arean av en trapets tar man medelv\u00e4rdet av basernas l\u00e4ngder multiplicerat med h\u00f6jden. Formeln kan skrivas s\u00e5 h\u00e4r:<\/p>\n

Area = (bas1 + bas2) \/ 2 \u00d7 h\u00f6jd<\/strong><\/p>\n

\"ber\u00e4kna<\/p>\n

H\u00e4r \u00e4r bas1 och bas2 l\u00e4ngderna p\u00e5 de parallella sidorna, och h\u00f6jden (h) \u00e4r det vinkelr\u00e4ta avst\u00e5ndet mellan de parallella sidorna (allts\u00e5 ”hur h\u00f6gt” trapetsen \u00e4r fr\u00e5n ena basen till den andra). Om till exempel en trapets har en bas som \u00e4r 6 m, den andra basen 4 m, och h\u00f6jden \u00e4r 3 m, d\u00e5 blir arean 6+4\/2 \u00d7 3 = 5 \u00d7 3 = 15 kvadratmeter (15 m\u00b2).<\/p>\n

Area i vardagen<\/h2>\n

Area \u00e4r inte bara ett abstrakt mattetal – det anv\u00e4nds flitigt i vardagslivet. Till exempel, n\u00e4r man ska k\u00f6pa f\u00e4rg f\u00f6r att m\u00e5la en v\u00e4gg beh\u00f6ver man veta v\u00e4ggens area f\u00f6r att ber\u00e4kna hur mycket f\u00e4rg som g\u00e5r \u00e5t. En v\u00e4gg med st\u00f6rre area kr\u00e4ver mer f\u00e4rg. P\u00e5 liknande s\u00e4tt m\u00e5ste en golvl\u00e4ggare k\u00e4nna till golvets area i ett rum f\u00f6r att veta hur m\u00e5nga kvadratmeter golvmaterial som beh\u00f6vs.<\/p>\n

Ett annat vardagsexempel \u00e4r bostadsytan: L\u00e4genheter och hus m\u00e4ts ofta i kvadratmeter f\u00f6r att ange hur stor boytan \u00e4r. Om n\u00e5gon s\u00e4ger att deras rum \u00e4r 12 m\u00b2 s\u00e5 f\u00f6rst\u00e5r vi hur stort rummet \u00e4r. Inom lantbruk och geografi anv\u00e4nds ocks\u00e5 area; exempelvis m\u00e4ts \u00e5kerytor och skogsomr\u00e5den i hektar (d\u00e4r 1 hektar \u00e4r 10\u202f000 m\u00b2).<\/p>\n

Som student \u00e4r det nyttigt att f\u00f6rst\u00e5 area, f\u00f6r det hj\u00e4lper dig att l\u00f6sa problem b\u00e5de i matematikb\u00f6ckerna och i verkliga situationer. Genom att kunna r\u00e4kna ut area f\u00f6r olika former kan du uppskatta allt fr\u00e5n hur mycket matta du beh\u00f6ver till ditt sovrum, till hur stor en park \u00e4r. Ofta kombineras detta med andra omr\u00e5den; vill du till exempel veta hur stor andel av ett rum mattan t\u00e4cker, eller hur mycket hyran \u00f6kar per kvadratmeter, har du stor nytta av procentr\u00e4kning<\/a>. Area \u00e4r helt enkelt ett grundl\u00e4ggande begrepp som kopplar samman matematiken med v\u00e5r fysiska omv\u00e4rld p\u00e5 ett praktiskt s\u00e4tt. Vill du l\u00e4ra dig mer om matte p\u00e5 ett enkelt och roligt s\u00e4tt kan du l\u00e4sa vidare p\u00e5 v\u00e5r sida om matematik<\/a> hos Studybuddy.<\/p>","protected":false},"excerpt":{"rendered":"

Vad \u00e4r area? Area \u00e4r ett m\u00e5tt p\u00e5 hur stor en yta \u00e4r. Inom geometrin anv\u00e4nder vi area f\u00f6r att beskriva storleken p\u00e5 tv\u00e5dimensionella figurer, till exempel hur stor ytan av en rektangel eller cirkel \u00e4r. Arean m\u00e4ts i kvadratenheter, vilket betyder att man anger arean i rutor av en viss l\u00e4ngd. Vanliga enheter f\u00f6r […]<\/p>\n","protected":false},"author":9,"featured_media":55699,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2006],"tags":[2467],"class_list":["post-55690","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-guide-studiehjalp","tag-area"],"acf":[],"yoast_head":"\nArea - r\u00e4kna ut arean av alla figurer | Studybuddy L\u00e4xhj\u00e4lp<\/title>\n<meta name=\"description\" content=\"S\u00e5 ber\u00e4knar du area f\u00f6r olika former. 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