{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T15:47:18+00:00","modifiedTime":"2016-03-26T15:47:18+00:00","timestamp":"2022-09-14T18:06:07+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Study Skills & Test Prep","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33772"},"slug":"study-skills-test-prep","categoryId":33772},{"name":"ACT","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33775"},"slug":"act","categoryId":33775}],"title":"Plane Geometry Formulas You Must Know for the ACT","strippedTitle":"plane geometry formulas you must know for the act","slug":"plane-geometry-formulas-you-must-know-for-the-act","canonicalUrl":"","seo":{"metaDescription":"Some of the questions on the ACT Math test deal with plane geometry. Plane geometry is chock-full of useful formulas. If you can’t commit all these formulas to ","noIndex":0,"noFollow":0},"content":"<p>Some of the questions on the ACT Math test deal with plane geometry. Plane geometry is chock-full of useful formulas. If you can’t commit all these formulas to memory and need to prioritize them, memorize everything up to the circumference of a circle. These are the must-know formulas for geometry. Then, if you have time, work your way forward from there.</p>\n<ul class=\"level-one\">\n <li><p class=\"first-para\"><b>Interior angles of a polygon</b> (the total of all angles inside the polygon):</p>\n<p class=\"child-para\">Total measure of the interior angles = 180(Number of angles – 2)</p>\n </li>\n <li><p class=\"first-para\"><b>Area of a triangle:</b></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355814.image0.png\" width=\"59\" height=\"37\" alt=\"image0.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Pythagorean theorem (where <i>a</i> and <i>b</i> are the legs, and <i>c</i> is the hypotenuse):</b></p>\n<p class=\"child-para\"><i>a</i><i><sup>2</sup></i> + <i>b</i><i><sup>2</sup></i> = <i>c</i><i><sup>2</sup></i></p>\n </li>\n <li><p class=\"first-para\"><b>Area and perimeter of a square of side <i>s</i>:</b></p>\n<p class=\"child-para\"><i>A</i> = <i>s</i><sup>2</sup></p>\n<p class=\"child-para\"><i>P</i> = 4<i>s</i></p>\n </li>\n <li><p class=\"first-para\"><b>Area and perimeter of a rectangle of sides <i>l</i> and <i>w</i>:</b></p>\n<p class=\"child-para\"><i>A</i> = <i>lw</i></p>\n<p class=\"child-para\"><i>P</i> = 2<i>l</i> + 2<i>w</i></p>\n </li>\n <li><p class=\"first-para\"><b>Area of a parallelogram:</b></p>\n<p class=\"child-para\"><i>A</i> = <i>bh</i></p>\n </li>\n <li><p class=\"first-para\"><b>Area of a trapezoid:</b></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355815.image1.png\" width=\"87\" height=\"41\" alt=\"image1.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Diameter, area, and circumference of a circle:</b></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355816.image2.png\" width=\"55\" height=\"80\" alt=\"image2.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Arc length of a circle:</b></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355817.image3.png\" width=\"169\" height=\"37\" alt=\"image3.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Volume and surface area of a cube:</b></p>\n<p class=\"child-para\"><i>V</i> = <i>s</i><sup>3</sup></p>\n<p class=\"child-para\"><i>A</i> = 6<i>s</i><sup>2</sup></p>\n </li>\n <li><p class=\"first-para\"><b>Volume and surface area of a box:</b></p>\n<p class=\"child-para\"><i>V</i> = <i>lwh</i></p>\n<p class=\"child-para\"><i>A</i> = 2<i>lw</i> + 2<i>lh</i> + 2<i>wh</i></p>\n </li>\n <li><p class=\"first-para\"><b>Volume and surface area of a sphere:</b></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355818.image4.png\" width=\"67\" height=\"67\" alt=\"image4.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Volume of a right prism: </b></p>\n<p class=\"child-para\"><i>V</i> = <i>A</i><i><sub>b</sub></i><i>h</i></p>\n </li>\n <li><p class=\"first-para\"><b>Volume of a pyramid:</b></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355819.image5.png\" width=\"68\" height=\"37\" alt=\"image5.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Volume of a cylinder:</b></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355820.image6.png\" width=\"63\" height=\"24\" alt=\"image6.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Volume of a cone:</b></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355821.image7.png\" width=\"75\" height=\"37\" alt=\"image7.png\"/>\n </li>\n</ul>","description":"<p>Some of the questions on the ACT Math test deal with plane geometry. Plane geometry is chock-full of useful formulas. If you can’t commit all these formulas to memory and need to prioritize them, memorize everything up to the circumference of a circle. These are the must-know formulas for geometry. Then, if you have time, work your way forward from there.</p>\n<ul class=\"level-one\">\n <li><p class=\"first-para\"><b>Interior angles of a polygon</b> (the total of all angles inside the polygon):</p>\n<p class=\"child-para\">Total measure of the interior angles = 180(Number of angles – 2)</p>\n </li>\n <li><p class=\"first-para\"><b>Area of a triangle:</b></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355814.image0.png\" width=\"59\" height=\"37\" alt=\"image0.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Pythagorean theorem (where <i>a</i> and <i>b</i> are the legs, and <i>c</i> is the hypotenuse):</b></p>\n<p class=\"child-para\"><i>a</i><i><sup>2</sup></i> + <i>b</i><i><sup>2</sup></i> = <i>c</i><i><sup>2</sup></i></p>\n </li>\n <li><p class=\"first-para\"><b>Area and perimeter of a square of side <i>s</i>:</b></p>\n<p class=\"child-para\"><i>A</i> = <i>s</i><sup>2</sup></p>\n<p class=\"child-para\"><i>P</i> = 4<i>s</i></p>\n </li>\n <li><p class=\"first-para\"><b>Area and perimeter of a rectangle of sides <i>l</i> and <i>w</i>:</b></p>\n<p class=\"child-para\"><i>A</i> = <i>lw</i></p>\n<p class=\"child-para\"><i>P</i> = 2<i>l</i> + 2<i>w</i></p>\n </li>\n <li><p class=\"first-para\"><b>Area of a parallelogram:</b></p>\n<p class=\"child-para\"><i>A</i> = <i>bh</i></p>\n </li>\n <li><p class=\"first-para\"><b>Area of a trapezoid:</b></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355815.image1.png\" width=\"87\" height=\"41\" alt=\"image1.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Diameter, area, and circumference of a circle:</b></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355816.image2.png\" width=\"55\" height=\"80\" alt=\"image2.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Arc length of a circle:</b></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355817.image3.png\" width=\"169\" height=\"37\" alt=\"image3.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Volume and surface area of a cube:</b></p>\n<p class=\"child-para\"><i>V</i> = <i>s</i><sup>3</sup></p>\n<p class=\"child-para\"><i>A</i> = 6<i>s</i><sup>2</sup></p>\n </li>\n <li><p class=\"first-para\"><b>Volume and surface area of a box:</b></p>\n<p class=\"child-para\"><i>V</i> = <i>lwh</i></p>\n<p class=\"child-para\"><i>A</i> = 2<i>lw</i> + 2<i>lh</i> + 2<i>wh</i></p>\n </li>\n <li><p class=\"first-para\"><b>Volume and surface area of a sphere:</b></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355818.image4.png\" width=\"67\" height=\"67\" alt=\"image4.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Volume of a right prism: </b></p>\n<p class=\"child-para\"><i>V</i> = <i>A</i><i><sub>b</sub></i><i>h</i></p>\n </li>\n <li><p class=\"first-para\"><b>Volume of a pyramid:</b></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355819.image5.png\" width=\"68\" height=\"37\" alt=\"image5.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Volume of a cylinder:</b></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355820.image6.png\" width=\"63\" height=\"24\" alt=\"image6.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Volume of a cone:</b></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355821.image7.png\" width=\"75\" height=\"37\" alt=\"image7.png\"/>\n </li>\n</ul>","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <b>Mark Zegarelli</b> is a professional writer with degrees in both English and Math from Rutgers University. He has earned his living for many years writing vast quantities of logic puzzles, a hefty chunk of software documentation, and the occasional book or film review. Along the way, he’s also paid a few bills doing housecleaning, decorative painting, and (for ten hours) retail sales. He likes writing best, though.","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/9399"}}],"primaryCategoryTaxonomy":{"categoryId":33775,"title":"ACT","slug":"act","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33775"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[{"articleId":208624,"title":"ACT Math For Dummies Cheat Sheet","slug":"act-math-for-dummies-cheat-sheet","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208624"}},{"articleId":187911,"title":"Solving Math Word Problems on the ACT","slug":"solving-math-word-problems-on-the-act","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187911"}},{"articleId":187910,"title":"Using Charts and Pictures to Answer ACT Math Questions","slug":"using-charts-and-pictures-to-answer-act-math-questions","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187910"}},{"articleId":187907,"title":"Test-Taking Strategies for the Math Portion of the ACT","slug":"test-taking-strategies-for-the-math-portion-of-the-act","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187907"}},{"articleId":173579,"title":"Practice Mathematics Test 2 for the ACT — 60 Questions","slug":"practice-mathematics-test-2-for-the-act-60-questions","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/173579"}}],"fromCategory":[{"articleId":294142,"title":"ACT Prep 2023 For Dummies Cheat Sheet","slug":"act-prep-2023-for-dummies-cheat-sheet","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/294142"}},{"articleId":268046,"title":"How to Organize Your ACT Essay","slug":"how-to-organize-your-act-essay","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/268046"}},{"articleId":268043,"title":"How to Write a Great ACT Essay","slug":"how-to-write-a-great-act-essay","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/268043"}},{"articleId":268033,"title":"ACT Geometry Test: Triangle Trauma","slug":"act-geometry-test-triangle-trauma","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/268033"}},{"articleId":268023,"title":"ACT Geometry Test: Analyzing Angles","slug":"act-geometry-test-analyzing-angles","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/268023"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":281928,"slug":"act-math-for-dummies","isbn":"9781118001547","categoryList":["academics-the-arts","study-skills-test-prep","act"],"amazon":{"default":"https://www.amazon.com/gp/product/1118001540/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1118001540/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1118001540-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1118001540/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1118001540/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/act-math-for-dummies-cover-9781118001547-193x255.jpg","width":193,"height":255},"title":"ACT Math For Dummies","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"<p><b data-author-id=\"9399\">Mark Zegarelli</b> is the author of <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies</i> (both from Wiley), and five other books on basic math, calculus, and logic. He holds degrees in both English and math from Rutgers University and is a math tutor and teacher. </p>","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <b>Mark Zegarelli</b> is a professional writer with degrees in both English and Math from Rutgers University. He has earned his living for many years writing vast quantities of logic puzzles, a hefty chunk of software documentation, and the occasional book or film review. Along the way, he’s also paid a few bills doing housecleaning, decorative painting, and (for ten hours) retail sales. He likes writing best, though.","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/9399"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{"key":"cat","values":["academics-the-arts","study-skills-test-prep","act"]},{"key":"isbn","values":["9781118001547"]}]\" id=\"du-slot-6322180f5b1ad\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{"key":"cat","values":["academics-the-arts","study-skills-test-prep","act"]},{"key":"isbn","values":["9781118001547"]}]\" 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Plane Geometry Formulas You Must Know for the ACT

By: Mark Zegarelli and

Updated: 03-26-2016

From The Book: ACT Math For Dummies

ACT Math For Dummies

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Some of the questions on the ACT Math test deal with plane geometry. Plane geometry is chock-full of useful formulas. If you can’t commit all these formulas to memory and need to prioritize them, memorize everything up to the circumference of a circle. These are the must-know formulas for geometry. Then, if you have time, work your way forward from there.

Interior angles of a polygon (the total of all angles inside the polygon):

Total measure of the interior angles = 180(Number of angles – 2)
Area of a triangle:
Pythagorean theorem (where a and b are the legs, and c is the hypotenuse):

a² + b² = c²
Area and perimeter of a square of side s:

A = s²

P = 4s
Area and perimeter of a rectangle of sides l and w:

A = lw

P = 2l + 2w
Area of a parallelogram:

A = bh
Area of a trapezoid:
Diameter, area, and circumference of a circle:
Arc length of a circle:
Volume and surface area of a cube:

V = s³

A = 6s²
Volume and surface area of a box:

V = lwh

A = 2lw + 2lh + 2wh
Volume and surface area of a sphere:
Volume of a right prism:

V = A_bh
Volume of a pyramid:
Volume of a cylinder:
Volume of a cone:

About This Article

This article is from the book:

ACT Math For Dummies ,

About the book author:

Mark Zegarelli is the author of Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies (both from Wiley), and five other books on basic math, calculus, and logic. He holds degrees in both English and math from Rutgers University and is a math tutor and teacher.

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