[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-297575-105":59,"doc-detail-297575-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","area-and-perimeter-dimensions-and-volume-learn-perimeter-area-and-volume-for-2-d-and-3-d-shapes","Area and Perimeter, Dimensions and Volume - Learn perimeter, area and volume for 2-D and 3-D shapes","","Understanding perimeter, area, and volume and how they relate to the dimensions of 2-D and 3-D shapes. Covers finding perimeters by adding side lengths and converting between length units. Explains circle circumference and area using C = πd and A = πr², plus metric unit conversion. Includes surface area calculations using nets, plus volume formulas for cuboids, prisms, and cylinders. Guides checking units and deciding whether formulas represent L, L², or L³.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/area-and-perimeter-dimensions-and-volume-learn-perimeter-area-and-volume-for-2-d-and-3-d-shapes/297575/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/area-and-perimeter-dimensions-and-volume-learn-perimeter-area-and-volume-for-2-d-and-3-d-shapes/297575.png","ImageObject",300,407,{"name":92,"@type":93},"Fahsai","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is perimeter and how is it calculated for 2-D shapes?","Question",{"text":113,"@type":114},"Perimeter measures the distance around the outline. It is found by adding the lengths of the sides, including any missing sides using the given information.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do you calculate the area of a circle?",{"text":118,"@type":114},"Use A = πr², where r is the radius. Substitute the radius value and compute the result using π (or an estimate like 3·14).",{"name":120,"@type":111,"acceptedAnswer":121},"How can you tell whether a formula gives length, area, or volume?",{"text":122,"@type":114},"Count the dimensions involved: perimeter is L (one length), area is L² (two lengths multiplied), and volume is L³ (three lengths multiplied). Never mix dimensions in a single calculation.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},297575,1790467231,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":24},549768702563,"https://ap-avatar.wpscdn.com/avatar/8000c4aa63b76e948b?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786536092046926083","Area and perimeter, dimensions and volume  \nUnderstanding the difference between perimeter, area and volume. Calculating the perimeter, area and volume of different 2-D and 3-D shapes .  \nPerimeter  \nThis measures the distance around the outline of a shape.  \n9 m  \n\n| 5·5 m | Find the length of 9 – 6·2 = 2·8 m |\n| --- | --- |\n|  | 6·2 m 13 m |\n|  |  |\n\nany missing sides.  \n13 – 5·5 = 7·5 m  \nAdd the lengths of the sides.  \n9 + 5·5 + 2·8 + 7·5 + 6·2 + 13 = 44 m  \nPerimeter is measured in units as mm, cm, m...  \nConverting between measurements of length  \n÷10 ÷100 ÷1000  \nmm cm m km  \n× 10 × 100 × 1000  \nArea  \nCircumference of a circle  \nThe perimeter of a circle is called the circumference.  \nUsing C to represent circumference, and d to represent diameter, we write the formula for the circumference of acircle as: C = πd  \nSince the diameter is twice as long asthe radius (d = 2r), we can also write the formula for the circumference:  \nC = 2πr  \nWe can use π in our calculators, or we can use an estimate of 3∙14.  \nArea of a Circle  \nUsing A to represent area and r to represent radius, the formula for the area of a circle is:  \nA = πr2  \n10cm  \nC = 2πr  \n= 2 × 3∙14 × 10 = 62∙8cm  \nA = πr2  \n= 3∙14 × 102  \n= 3∙14cm2  \nArea This measures the amount of space within a 2-D shape. Area of a Rectangle  \nCheck that you can:  \n• recognize 2-D shapes and their properties  \n• recognize 3-D shapes and their properties  \n• draw nets of 3-D shapes  \n• substitute values into a formula  \n• understand the relationship between units of the metric system.  \nREMEMBER!  \nDon’t forget to use the information you are given to calculate the lengths of any missing sides.  \nArea and perimeter, dimensions and volume  \nUnderstanding the difference between perimeter, area and volume. Calculating the perimeter, area and volume of different 2-D and 3-D shapes .  \nCheck that you can:  \n• calculate the area of different 2-D shapes.  \nSurface Area This is the total area of every surface (face) of a 3-D shape.  \nIt is useful to consider the net of the 3-D shape, to find the area of each face, in order to calculate the total surface area.  \n7 m  \n\n| 5 m | C | 3 m |  |\n| --- | --- | --- | --- |\n| A | B | A | B |\n| 5 m | C |  |  |\n\n3 m  \n7 m  \nArea of A = 7 × 5 = 35 m2 Area of B = 7 × 3 = 21 m2  \nArea ofC = 3 × 5 = 15 m2  \nTotal surface area = 2 × (35 + 21 + 15)= 142 m2  \nREMEMBER!  \n• Take care to include every side of the shape when calculating surface area.  \n• Draw a sketch of the sides you are using for your calculation, and draw on the dimensions you need.  \nVolume This measures the amount of space within a 3D shape. Volume of a Cuboid  \nVolume of a cuboid = length × width × height  \n= 8 × 5 × 3  \n= 120 cm2  \nVolume of a Prism  \n8cm  \nVolume of a prism = area of the cross-section × length = 200 × 57  \n= 11400 mm3  \nVolume of a Cylinder  \n5cm  \n57mm Area = 200mm2  \nVolume of a cylinder = area of the cross-section × length  \n= πr2 × l = 3∙14 × 22 × 5 = 62∙8 cm2  \n2cm  \n5cm  \nVolume is measured in [units](units3 e.g. mm3)[3](units3 e.g. mm3)[ e.g. mm](units3 e.g. mm3)[3](units3 e.g. mm3), cm3, m3 ...  \nConverting between measurements of volume  \nE. g. Convert 5∙5 mm3 to cm3.  \n5∙5 × 100³ = 5∙5 × 1 000 000 = 5 500 000 cm3  \nmm3  \n÷103  \n× 103  \ncm3  \n÷1003 ÷10003  \nm3 km3  \n× 1003 × 10003  \nRemember to check the measurements are in the same units before adding or multiplying to find perimeter, area or volume.  \nDimensions and formulae  \nWe can decide if a formula is for a perimeter, area or volume by looking at the dimensions involved.  \nWe know that:  \n• perimeter is a measurement of length (L): 1 dimension  \n• area is given by a length × length (L2): 2 dimensions  \n• volume is given by a length × length × length (L3): 3 dimensions.  \nDeciding if a formula is length, area or volume formula  \nExample 1:  \nPerimeter of a rectangle = 2 × length + 2 × width  \n= 2l + 2w  \nRemember, numbers have no dimension.  \nSo, the expression 2l + 2w is simply a length and has one di","cbCaigKAqiuqdJDX","https://ap.wps.com/l/cbCaigKAqiuqdJDX","pdf",1496723,"English","# Perimeter\n## Calculating perimeter and missing sides\n## Converting length units\n# Area\n## Circle circumference and area (C = πd, A = πr²)\n## Area of rectangles and metric units\n## Surface area of 3-D shapes\n# Volume\n## Volume of cuboids and prisms\n## Volume of cylinders\n## Converting volume units\n# Dimensions and formulas\n## Identifying L, L² and L³ formulas\n## Preventing mixed-dimension errors","[{\"question\":\"What is perimeter and how is it calculated for 2-D shapes?\",\"answer\":\"Perimeter measures the distance around the outline. It is found by adding the lengths of the sides, including any missing sides using the given information.\"},{\"question\":\"How do you calculate the area of a circle?\",\"answer\":\"Use A = πr², where r is the radius. Substitute the radius value and compute the result using π (or an estimate like 3·14).\"},{\"question\":\"How can you tell whether a formula gives length, area, or volume?\",\"answer\":\"Count the dimensions involved: perimeter is L (one length), area is L² (two lengths multiplied), and volume is L³ (three lengths multiplied). Never mix dimensions in a single calculation.\"}]","Area and Perimeter, Dimensions and Volume - Learn perimeter, area and volume for 2-D and 3-D shapes | PDF",1789745869]