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It also provides surface area and volume formulas for core 3D solids including cube, prism, sphere, cylinder, cone, frustum, pyramid, spherical segment, torus, tetrahedron, octahedron, dodecahedron, and icosahedron.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/technology/","Technology",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/plane-shapes-and-solid-shapes-formulas/671025/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/plane-shapes-and-solid-shapes-formulas/671025.png","ImageObject",300,407,{"name":42,"@type":43},"Jiven","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-02","2026-11-01",true,{"@type":52,"interactionType":53,"userInteractionCount":26},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"What symbols and quantities are used for plane and solid geometry formulas?","Question",{"text":62,"@type":63},"The sheet uses A for area, P for perimeter, S for area (for some shapes), and V for volume. It also refers to internal and external angles and diagonal counts for polygons.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"Which 2D shapes and measures are covered under plane shapes?",{"text":67,"@type":63},"It includes quadrilaterals like parallelogram and trapezoid, multiple triangle types (equilateral, isosceles, scalene, right), regular pentagon/hexagon/octagon, regular polygons, and several circular figures such as circular sector, segment, circular triangle, circular trapezoid, and annulus.",{"name":69,"@type":60,"acceptedAnswer":70},"Which 3D solids have formulas for surface area and volume?",{"text":71,"@type":63},"It lists cube, right prism, sphere, cylinder, circular cone, circular cone frustum, pyramid, spherical segment, torus, tetrahedron, octahedron, dodecahedron, and icosahedron, with corresponding area and volume expressions.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},671025,1793573403,{"code":4,"msg":81,"data":82},"success",[83,87,91,95,100,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & 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\n\n| | A 􀀁 a 2\u003Cbr>P 􀀁 4a | Internal angle 􀀃 􀀁 90􀀂 External angle 􀀄 􀀁 90􀀂 Number of diagonals ND 􀀁 2 |\n| --- | --- | --- |\n| | A 􀀁 b·h\u003Cbr>P 􀀁 2b 􀀅 2h |  |\n| Parallelogram\u003Cbr>| A 􀀁 b·h\u003Cbr>P 􀀁 2b 􀀅 2a |  |\n| | A 􀀁 d2·DP 􀀁 4a\u003Cbr>4a2 􀀁 d 2 􀀅 D2 |  |\n| Trapezoid (trapezium)\u003Cbr>| A 􀀁 b~~ ~~􀀅2B h\u003Cbr>P 􀀁 a 􀀅 b 􀀅 B 􀀅 c |  |\n\n[www.vaxasoftware.com](www.vaxasoftware.com)  \n\n| Right trapezoid\u003Cbr>| A 􀀁 b~~ ~~􀀅2B h P 􀀁 a 􀀅 b 􀀅 B 􀀅 h\u003Cbr>a 2 􀀁 (B 􀀆 b)2 􀀅 h2 |  |\n| --- | --- | --- |\n| Equilateral triangle\u003Cbr>A 􀀁 a ·h 􀀁   3  a 2 Internal angle 􀀃 􀀁 60􀀂\u003Cbr>2 4\u003Cbr>P 􀀁 3a , h 􀀁 23~~ ~~ a External angle 􀀄 􀀁 120􀀂\u003Cbr>Number of diagonals ND 􀀁 0\u003Cbr>|  |  |\n| Isosceles triangle\u003Cbr>| S 􀀁 b·h 􀀁 a ·b·sin A\u003Cbr>2 2\u003Cbr>P 􀀁 2a 􀀅 b , h 􀀁 a · sin A\u003Cbr>4a2 􀀁 4h2 􀀅 b2 |  |\n| Scalene triangle\u003Cbr>| S 􀀁 b2·h\u003Cbr>P 􀀁 a 􀀅 b 􀀅 ch 􀀁 c · sin A 􀀁 a · sin C |  |\n| Right triangle b·a\u003Cbr>S 􀀁  2 \u003Cbr>P 􀀁 a 􀀅 b 􀀅 c\u003Cbr>Pythagorean theorem c 2 􀀁 a 2 􀀅 b2\u003Cbr>h2 􀀁 m 􀀇 n\u003Cbr>2\u003Cbr>a 􀀁 m 􀀇 c\u003Cbr>b2 􀀁 n 􀀇 c\u003Cbr>c 􀀁 m 􀀅 n\u003Cbr>|  | a 􀀁 c · sen A 􀀁 c · cos B\u003Cbr>b 􀀁 c · sen B 􀀁 c · cos A |\n\n\n| Regular pentagon\u003Cbr>| A 􀀁 5a·b 􀀁 5 r 2 ~~ ~~10 􀀅 25 􀀁 5 r 2 ·sin 72􀀂 2 8 2 |  |  |  |\n| --- | --- | --- | --- | --- |\n|  | P 􀀁 5b 4r2 􀀁 4a2 􀀅 b2\u003Cbr>b 􀀁 r2 ~~ ~~10 􀀆 25 􀀁 2r·sin 36􀀂\u003Cbr>a 􀀁 r4 ~~ ~~6 􀀅 25 􀀁 r ·cos 36􀀂 |  | Internal angle 􀀃 􀀁 108􀀂 External angle 􀀄 􀀁 72􀀂 Number of diagonals ND 􀀁 5 |  |\n| Regular hexagon\u003Cbr>| A 􀀁 323~~ ~~ b2 􀀁 3b2 ·sin 60􀀂 P 􀀁 6ba 􀀁 23~~ ~~ b 􀀁 b·cos30􀀂 | Internal angle 􀀃 􀀁 120􀀂 External angle 􀀄 􀀁 60􀀂 Number of diagonals ND 􀀁 9 |  |  |\n| Regular octagon\u003Cbr>| A 􀀁 4·a ·b 􀀁 8·a 2 ·tan 22.5􀀂 􀀁 􀀈8 2 􀀆 8􀀉 a 2 􀀁  2b2  􀀁  2b2 \u003Cbr>tan 22 .5􀀂 2 􀀆1 |  |  |  |\n|  | P 􀀁 8·b 􀀁 16·a ·tan22 .5􀀂 a 􀀁 r ·cos22 .5􀀂 b 􀀁 2r·sin22.5􀀂 | Internal angle 􀀃 􀀁 135􀀂 External angle 􀀄 􀀁 45􀀂 Number of diagonals ND 􀀁 20 |  |  |\n| Regular polygon (n sides)\u003Cbr>| n ·a ·b 2 180􀀂 A 􀀁  2  􀀁 n ·a ·tan~~ ~~n~~ ~~\u003Cbr>P 􀀁 n ·b 􀀁 2n ·a ·tan  180􀀂\u003Cbr>n\u003Cbr>a 􀀁 r ·cos ~~ ~~180n􀀂~~ ~~ b 􀀁 2r·sin ~~ ~~180n􀀂 |  |  | Internal angle :(n 􀀆 2)·180􀀂\u003Cbr>􀀃 􀀁\u003Cbr>n External angle :\u003Cbr>􀀄 􀀁 180􀀂 􀀆 􀀃\u003Cbr>Number of diagonals : ND 􀀁 n ·(n 􀀆 3)\u003Cbr>2 |\n| | A 􀀁 π r 2\u003Cbr>P 􀀁 2π r |  |  |  |\n\n[www.vaxasoftware.com](www.vaxasoftware.com)  \n\n| Circular sector\u003Cbr>| 2 􀀃 A 􀀁 π r 360􀀂 |\n| --- | --- |\n|  | L 􀀁 π r 􀀃  180􀀂 |\n|  | P 􀀁 2r 􀀅 L 􀀃 is expressed in sexagesimal degrees |\n| Circular segment\u003Cbr>| 2 􀀏 π ·􀀃 sin 􀀃 􀀌 A 􀀁 r 􀀎􀀍 360􀀂 􀀆  2  􀀋􀀊\u003Cbr>h 􀀁 r􀀍􀀏􀀎1 􀀆 cos ~~ ~~􀀃2~~ ~~ 􀀌􀀋􀀊 c 􀀁 2r ·sin ~~ ~~􀀃2~~ ~~ L 􀀁 π r ~~ ~~1􀀃80􀀂 P 􀀁 L 􀀅 c , r 􀀁 h2 􀀅 c28h~~ ~~ 􀀃 is expressed in sexagesimal degrees |\n| Circular triangle\u003Cbr>| A 􀀁 r 2 sin2􀀃~~ ~~ c 􀀁 2r·sin ~~ ~~􀀃2 |\n|  | P 􀀁 2r 􀀅 c 􀀃 is expressed in sexagesimal degrees |\n| Circular trapezoid\u003Cbr>| AP 􀀁􀀁 π2R(2Rrr2)􀀉 33􀀃60􀀃60􀀂􀀂  􀀅 2(R 􀀆 r)\u003Cbr>􀀃 is expressed in sexagesimal degrees |\n| Annulus\u003Cbr>| A 􀀁 π 􀀈R 2 􀀆 r2 􀀉 P 􀀁 2π (R 􀀅 r) |\n\n[www.vaxasoftware.com](www.vaxasoftware.com)  \n\n| | A 􀀁 π a·b P 􀀐 π (a 􀀅 b)\u003Cbr>P 􀀁 4􀀑0π / 2 ~~ ~~a 2sin 2t 􀀅 b2 cos2 t dt |\n| --- | --- |\n\nSolid shapes  \n\n| Cube (hexahedron)\u003Cbr>| A 􀀁 6 a 2 AFACE 􀀁 a 2\u003Cbr>V 􀀁 a 3 |\n| --- | --- |\n| Right prism\u003Cbr>| A 􀀁 2a·b 􀀅 2a ·c 􀀅 2b·c\u003Cbr>V 􀀁 a ·b·c |\n| Sphere\u003Cbr>| A 􀀁 4π·r 2\u003Cbr>4π ·r 3 V 􀀁 ~~ ~~\u003Cbr>3 |\n| Cylinder\u003Cbr>| ATOTAL 􀀁 2π r (h 􀀅 r)\u003Cbr>ABASES 􀀁 2π r 2 ALATERAL 􀀁 2π r·h\u003Cbr>V 􀀁 π·r 2 ·h |\n\n[www.vaxasoftware.com](www.vaxasoftware.com)  \n\n| Circular cone\u003Cbr>| ATOTAL 􀀁 π r ·g 􀀅 π r 2 |\n| --- | --- |\n|  | ABASE 􀀁 π r 2 ALATERAL 􀀁 π r ·g |\n|  | π r2 ·h 2 2 2\u003Cbr>V 􀀁  3  g 􀀁 h 􀀅 r |\n| Circular cone frustum\u003Cbr>| ATOTAL 􀀁 π [(r 􀀅 R)·g 􀀅 r2 􀀅 R2 ] |\n|  | ATOP 􀀁 π r 2 ABASE 􀀁 π R2 ALATERAL 􀀁 π (r 􀀅 R)·g V 􀀁 π~~ ~~·h(R~~ ~~2~~ ~~􀀅r32~~ ~~􀀅~~ ~~r~~ ~~􀀇~~ ~~R)~~ ~~ g 2 􀀁 h2 􀀅 (R 􀀆 r)2 |\n| Pyramid\u003Cbr>| ATOTAL 􀀁 ALAT 􀀅 ABASEA 􀀁 PerimeterBASE ·hC\u003Cbr>LAT\u003Cbr>2\u003Cbr>A ·h V 􀀁  BASE \u003Cbr>3 |\n| Spherical segment\u003Cbr>| ATOTAL 􀀁 ALATERAL 􀀅 ABASE\u003Cbr>ABASE 􀀁 ~~ ~~π4c~~ ~~2~~ ~~ ALATERAL 􀀁 2π r·h 􀀁 π4 􀀈c2 􀀅 4h2 􀀉 V 􀀁 π6 h 􀀏􀀎􀀍 3c42~~ ~~ 􀀅 h2 􀀌􀀋􀀊 􀀁 π h2 􀀏􀀎􀀍 r 􀀆 h3~~ ~~ 􀀌􀀋􀀊 r 􀀁 h2 􀀅 c82h |\n| Torus\u003Cbr>| A 􀀁 π 2D·d 􀀁 π 2 (R 2 􀀆 r","cbCaiuQTR2d49KE1","https://ap.wps.com/l/cbCaiuQTR2d49KE1","pdf",602613,"English","# Plane shapes\n## Solid shapes","[{\"question\":\"What symbols and quantities are used for plane and solid geometry formulas?\",\"answer\":\"The sheet uses A for area, P for perimeter, S for area (for some shapes), and V for volume. It also refers to internal and external angles and diagonal counts for polygons.\"},{\"question\":\"Which 2D shapes and measures are covered under plane shapes?\",\"answer\":\"It includes quadrilaterals like parallelogram and trapezoid, multiple triangle types (equilateral, isosceles, scalene, right), regular pentagon/hexagon/octagon, regular polygons, and several circular figures such as circular sector, segment, circular triangle, circular trapezoid, and annulus.\"},{\"question\":\"Which 3D solids have formulas for surface area and volume?\",\"answer\":\"It lists cube, right prism, sphere, cylinder, circular cone, circular cone frustum, pyramid, spherical segment, torus, tetrahedron, octahedron, dodecahedron, and icosahedron, with corresponding area and volume expressions.\"}]","Plane shapes and solid shapes - formulas | PDF",18]