[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-571802-105":53,"doc-detail-571802-en":127},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":120,"head_meta":122,"extra_data":124,"updated_unix":126},105,"en","harolds-geometry-shape-formulas-cheat-sheet","Harold's Geometry Shape Formulas - Cheat Sheet","","This comprehensive geometry cheat sheet provides a structured reference for fundamental mathematical measurements, specifically covering perimeter, area, surface area, and volume. The document organizes formulas for a variety of two-dimensional shapes, including triangles, squares, rectangles, circles, and ellipses, alongside three-dimensional solids such as cubes, cylinders, cones, and spheres. It serves as an essential quick-reference guide for students and educators, clearly delineating the distinct units of measurement used for linear dimensions, surface area, and three-dimensional capacity. By consolidating complex geometric equations into easy-to-read tables, the document enables efficient problem-solving and academic review of spatial properties and volumetric calculations. The content is designed for clarity, ensuring that learners can quickly identify the correct formula for various geometric configurations encountered in mathematical coursework.",{"@graph":63,"@context":119},[64,80,102],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":51,"@type":70,"position":76},"https://docshare.wps.com/template/general/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/harolds-geometry-shape-formulas-cheat-sheet/571802/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/harolds-geometry-shape-formulas-cheat-sheet/571802.png","ImageObject",442,249,{"name":88,"@type":89},"Blue 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by the radius squared (πr²).","https://schema.org",{"og:url":78,"og:type":121,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":123,"canonical":78},"index,follow",{"doc_id":125,"site_id":56},571802,1792012881,{"code":4,"msg":5,"data":128},{"doc_id":125,"user_id":129,"nickname":88,"user_avatar":130,"doc_module":9,"category_id":50,"category_name":51,"doc_title":59,"doc_description":61,"doc_content":131,"file_id":132,"file_url":133,"file_type":134,"file_size":135,"view_count":101,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":73,"language":136,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":61,"update_tm":140,"read_time":9},962090760266,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Harold’s Geometry Shape Formulas  \nCheat Sheet  \n25 April 2025  \nPerimeter, Area, Surface Area, and Volume  \n\n| 2D Shapes | Perimeter (P, C) | Area (A) | 3D Shapes | Surface Area\u003Cbr>(SA) | Volume (V) |\n| --- | --- | --- | --- | --- | --- |\n| Units | Units | Units2 |  | Units2 | Units3 |\n| Example | Fence | Pasture |  | Paint It | Fill It |\n| Triangle\u003Cbr>| 􀜽 + 􀜾 + 􀜿 | 1 2\u003Cbr>􀜾ℎ | Triangular Prism\u003Cbr>| 􀜾ℎ + 􀝈􀜽 + 􀝈􀜾+ 􀝈􀜿 | 1 2\u003Cbr>􀜾ℎ􀝈 |\n| Square\u003Cbr>| 4􀜽 | 􀜽 2 | Cube\u003Cbr>| 6􀜽2 | 􀜽 3 |\n| Rectangle\u003Cbr>| 2 (􀝈 + 􀝓) | 􀝈􀝓 | Rectangular\u003Cbr>Prism\u003Cbr>| 2 (􀝈􀝓 + 􀝈ℎ+ 􀝓ℎ) | 􀝈􀝓ℎ |\n| Parallelogram\u003Cbr>| 2 (􀜽 + 􀜾) | 􀜾ℎ | Pyramid\u003Cbr>| 􀝈􀝓 + 􀝈􀜽􀝈􀜽: lateral area | 1 3\u003Cbr>􀝈􀝓ℎ |\n| Trapezoid\u003Cbr>| 􀜽 + 􀜾1 + 􀜾2 + 􀜿 | 12 (􀜾1 + 􀜾2)ℎ | Cone\u003Cbr>| 􀟨􀝎 2 + 􀟨􀝎􀝈 | 13 􀟨􀝎2 ℎ |\n\n\n| Rhombus\u003Cbr>| 4􀜮 | 12 􀝀 1 􀝀 2 | Cylinder\u003Cbr>| 2􀟨􀝎ℎ + 2􀟨􀝎2 | 􀟨􀝎2 ℎ |\n| --- | --- | --- | --- | --- | --- |\n| Regular Polygon\u003Cbr>| 􀝊􀝏 | 􀝊 (12 􀜽􀝏 )\u003Cbr>􀜽: apothem 􀝊: number of sides | Regular Prism\u003Cbr>| 􀝊􀜽􀜾 + 􀝊􀜾ℎ | 􀝊 2\u003Cbr>􀜽􀜾ℎ |\n| Circle\u003Cbr>| 2􀟨􀝎= 􀟨􀝀 | 􀟨􀝎 2 | Sphere\u003Cbr>| 4􀟨􀝎2 | 43 􀟨􀝎3 |\n| Circular Sector\u003Cbr>| 􀝏 + 2􀝎 | 􀟠 360∘ 􀟨􀝎2 | Spherical Segment\u003Cbr>| 􀟨 (􀜽2 + 􀜾 2 + 2􀝎ℎ)\u003Cbr>ℎ: height of segment | 16 􀟨ℎ(3􀜽2 + 3􀜾2 + ℎ2)  |\n| Ellipse\u003Cbr>| ≈ 􀟨 (􀜽 + 􀜾) | 􀟨􀜽􀜾 | Ellipsoid\u003Cbr>| See Knud Thomsen’s Formula | 43 􀟨􀜽􀜾􀜿 |\n\nSources:  \n• TPT, [https://www.teacherspayteachers.com/Product/Perimeter-Area-Surface-Area-Volume-Cheat-Sheet-](https://www.teacherspayteachers.com/Product/Perimeter-Area-Surface-Area-Volume-Cheat-Sheet-)[ ](https://www.teacherspayteachers.com/Product/Perimeter-Area-Surface-Area-Volume-Cheat-Sheet-)7377920","cbCaigmbFxcf5Ps8","https://ap.wps.com/l/cbCaigmbFxcf5Ps8","pdf",429739,"English","# 2D Shapes Formulas\n## Polygon and Circular Calculations\n# 3D Shapes Formulas\n## Surface Area and Volume References","[{\"question\":\"What are the primary geometric properties covered in the cheat sheet?\",\"answer\":\"The document covers perimeter, area, surface area, and volume formulas for various 2D and 3D shapes.\"},{\"question\":\"How is the volume of a sphere calculated according to this guide?\",\"answer\":\"The volume of a sphere is calculated using the formula 4/3 multiplied by pi multiplied by the radius cubed (4/3 πr³).\"},{\"question\":\"What formula is provided for the area of a circle?\",\"answer\":\"The area of a circle is defined by the formula pi multiplied by the radius squared (πr²).\"}]","Harold's Geometry Shape Formulas - Cheat Sheet | PDF",1791923776]