{"id":7597,"date":"2021-10-28T20:11:04","date_gmt":"2021-10-28T14:41:04","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7597"},"modified":"2022-01-16T17:08:50","modified_gmt":"2022-01-16T11:38:50","slug":"formula-for-surface-area-of-cuboid","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/","title":{"rendered":"Formula for Surface Area of Cuboid – Derivation and Examples"},"content":{"rendered":"

Here you will learn formula for surface area of cuboid (total surface area and lateral surface area), its derivation and examples based on it.<\/p>\n

Let’s begin – <\/p>\n

What is Cuboid ?<\/h2>\n

A cuboid is a three dimensional box. It is defined by the virtue of its length l, breadth b and height h. It can be visualised as a room which has length, breadth and height differerent from each other.<\/p>\n

Formula for Surface Area of Cuboid<\/h2>\n

(a) Total Surface Area of Cuboid (T.S.A)<\/strong><\/h4>\n
\n

T.S.A = 2(lb + bh + hl)<\/p>\n<\/blockquote>\n

(b) Lateral Surface Area of Cuboid (L.S.A)<\/strong><\/h4>\n
\n

L.S.A = 2(l + b)h<\/p>\n<\/blockquote>\n

Also Read<\/strong> : Formula for Volume of Cuboid \u2013 Derivation & Examples<\/a><\/p>\n

Derivation<\/strong> : <\/h3>\n

The outer surface of a cuboid is made up of six rectangles (rectangular regions, called the faces of the cuboid), whose areas can be found by multiplying length by breadth for each of them seperately and then adding the six areas together.<\/span><\/p>\n

Now, if we take the length of cuboid as <\/span>l<\/span>, breadth as <\/span>b <\/span>and the height as <\/span>h<\/span>, then<\/span><\/p>\n

The sum of areas of the six rectangles is:<\/span><\/p>\n

Area of rectangle 1 (= <\/span>l <\/span>\u00d7 <\/span>h<\/span>) <\/span>+ Area of rectangle 2 (= <\/span>l <\/span>\u00d7 <\/span>b<\/span>) + Area of rectangle 3 (= <\/span>l <\/span>\u00d7 <\/span>h<\/span>) + Area of rectangle 4 (= <\/span>l <\/span>\u00d7 <\/span>b<\/span>) + Area of rectangle 5 (= <\/span>b <\/span>\u00d7 <\/span>h<\/span>) + Area of rectangle 6 (= <\/span>b <\/span>\u00d7 <\/span>h<\/span>)<\/span><\/p>\n

= 2(<\/span>l <\/span>\u00d7 <\/span>b<\/span>) + 2(<\/span>b <\/span>\u00d7 <\/span>h<\/span>) + 2(<\/span>l <\/span>\u00d7 <\/span>h<\/span>)<\/span><\/p>\n

= 2(<\/span>lb <\/span>+ <\/span>bh <\/span>+ <\/span>hl<\/span>)<\/span><\/p>\n

This gives us: Total <\/strong><\/span>Surface Area of a Cuboid<\/strong> = 2(<\/span>lb <\/span>+ <\/span>bh <\/span>+ <\/span>hl<\/span>)<\/span><\/p>\n

Suppose, out of six faces of a cuboid, we only find the area of four faces, leaving the bottom and top faces. Then in such case, the area of these four faces is called the <\/span>lateral surface area <\/span>of the cuboid. So, <\/span>lateral surface area of a cuboid of length l, breadth b and height h is equal to 2lh + 2bh or 2<\/span>(<\/span>l + b<\/span>)<\/span>h<\/span>.<\/span><\/p>\n

Then  Lateral Surface Area<\/strong> = 2<\/span>(<\/span>l + b<\/span>)<\/span>h<\/span><\/p>\n

Example<\/span><\/strong> : If we have a cuboid whose length, breadth and height are 15 cm, 10 cm and 20 cm respectively, then find its total surface area.<\/span><\/p>\n

Solution<\/span><\/strong> : We have l = 15 cm , b = 10 cm and h = 20 cm<\/span><\/p>\n

Total Surface Area = 2[(15 \\(\\times\\) 10) + (10 \\(\\times\\) 20) + (20 \\(\\times\\) 15)] \\(cm^2\\)<\/span><\/p>\n

Total Surface Area = 2(150 + 200 + 300) \\(cm^2\\)<\/span><\/p>\n

= 2 \u00d7 650 \\(cm^2\\)<\/span><\/p>\n

= 1300 \\(cm^2\\)<\/span><\/p>\n\n\n

\n
Next – Formula for Surface Area of Cube<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn formula for surface area of cuboid (total surface area and lateral surface area), its derivation and examples based on it. Let’s begin –  What is Cuboid ? A cuboid is a three dimensional box. It is defined by the virtue of its length l, breadth b and height h. It can …<\/p>\n

Formula for Surface Area of Cuboid – Derivation and Examples<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[63],"tags":[680,681,679],"yoast_head":"\nFormula for Surface Area of Cuboid - Derivation and Examples<\/title>\n<meta name=\"description\" content=\"In this post you will learn formula for surface area of cuboid (total surface area and lateral surface area), its derivation and examples.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Formula for Surface Area of Cuboid - Derivation and Examples\" \/>\n<meta property=\"og:description\" content=\"In this post you will learn formula for surface area of cuboid (total surface area and lateral surface area), its derivation and examples.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-28T14:41:04+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-01-16T11:38:50+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Formula for Surface Area of Cuboid – Derivation and Examples\",\"datePublished\":\"2021-10-28T14:41:04+00:00\",\"dateModified\":\"2022-01-16T11:38:50+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/\"},\"wordCount\":376,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"keywords\":[\"lateral surface area of cuboid\",\"surface area of cuboid formula and derivation\",\"total surface area of cuboid\"],\"articleSection\":[\"Surface Area & Volumes\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/\",\"url\":\"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/\",\"name\":\"Formula for Surface Area of Cuboid - Derivation and Examples\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-10-28T14:41:04+00:00\",\"dateModified\":\"2022-01-16T11:38:50+00:00\",\"description\":\"In this post you will learn formula for surface area of cuboid (total surface area and lateral surface area), its derivation and examples.\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Formula for Surface Area of Cuboid – Derivation and Examples\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Formula for Surface Area of Cuboid - Derivation and Examples","description":"In this post you will learn formula for surface area of cuboid (total surface area and lateral surface area), its derivation and examples.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/","og_locale":"en_US","og_type":"article","og_title":"Formula for Surface Area of Cuboid - Derivation and Examples","og_description":"In this post you will learn formula for surface area of cuboid (total surface area and lateral surface area), its derivation and examples.","og_url":"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/","og_site_name":"Mathemerize","article_published_time":"2021-10-28T14:41:04+00:00","article_modified_time":"2022-01-16T11:38:50+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"Formula for Surface Area of Cuboid – Derivation and Examples","datePublished":"2021-10-28T14:41:04+00:00","dateModified":"2022-01-16T11:38:50+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/"},"wordCount":376,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"keywords":["lateral surface area of cuboid","surface area of cuboid formula and derivation","total surface area of cuboid"],"articleSection":["Surface Area & Volumes"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/","url":"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/","name":"Formula for Surface Area of Cuboid - Derivation and Examples","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2021-10-28T14:41:04+00:00","dateModified":"2022-01-16T11:38:50+00:00","description":"In this post you will learn formula for surface area of cuboid (total surface area and lateral surface area), its derivation and examples.","breadcrumb":{"@id":"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/formula-for-surface-area-of-cuboid\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"Formula for Surface Area of Cuboid – Derivation and Examples"}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/7597"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=7597"}],"version-history":[{"count":12,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/7597\/revisions"}],"predecessor-version":[{"id":9570,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/7597\/revisions\/9570"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=7597"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=7597"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=7597"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}