{"id":72864,"date":"2021-02-05T22:29:06","date_gmt":"2021-02-05T16:59:06","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=72864"},"modified":"2021-09-04T15:02:01","modified_gmt":"2021-09-04T09:32:01","slug":"rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c12-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-%e2%80%8cexercise%e2%80%8c-%e2%80%8c12-1-%e2%80%8csolutio","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c12-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-%e2%80%8cexercise%e2%80%8c-%e2%80%8c12-1-%e2%80%8csolutio\/","title":{"rendered":"RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c12 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c \u200cExercise\u200c \u200c12.1 \u200cSolutions\u200c"},"content":{"rendered":"\n<p>RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c12 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c \u200cExercise\u200c \u200c12.1 \u200cSolutions\u200c is concerned with Heron\u2019s formula. The students will study \u201chow to find the area of a triangle using heron\u2019s formula?\u201d with the help of several solved problems. The experts have used the step-by-step problem-solving methods of the examples mentioned in this article.<\/p>\n<p>Students can freely download RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c12 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c \u200cExercise\u200c \u200c12.1 \u200cSolutions\u200c PDF and grind their skills. The PDF consists of varieties of questions based on Heron\u2019s Formula. The questions were explained stepwise, which is easily understandable to the students. By practicing through PDF, learners will get to know the several types of questions that can be formed. Practicing with these problems help students to score well in the exam.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69dc5aed54421\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #000000;color:#000000\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-69dc5aed54421\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.kopykitab.com\/blog\/rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c12-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-%e2%80%8cexercise%e2%80%8c-%e2%80%8c12-1-%e2%80%8csolutio\/#download-rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c12-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-%e2%80%8cexercise%e2%80%8c-%e2%80%8c121-%e2%80%8csolutions%e2%80%8c-pdf\" title=\"Download RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c12 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c \u200cExercise\u200c \u200c12.1 \u200cSolutions\u200c PDF\">Download RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c12 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c \u200cExercise\u200c \u200c12.1 \u200cSolutions\u200c PDF<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c12-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-%e2%80%8cexercise%e2%80%8c-%e2%80%8c12-1-%e2%80%8csolutio\/#important-definitions-rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c12-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-%e2%80%8cexercise%e2%80%8c-%e2%80%8c121-%e2%80%8csolutions%e2%80%8c\" title=\"Important Definitions RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c12 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c \u200cExercise\u200c \u200c12.1 \u200cSolutions\u200c\">Important Definitions RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c12 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c \u200cExercise\u200c \u200c12.1 \u200cSolutions\u200c<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c12-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-%e2%80%8cexercise%e2%80%8c-%e2%80%8c12-1-%e2%80%8csolutio\/#heron%e2%80%99s-formula\" title=\"Heron\u2019s Formula\">Heron\u2019s Formula<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c12-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-%e2%80%8cexercise%e2%80%8c-%e2%80%8c12-1-%e2%80%8csolutio\/#examples-of-heron%e2%80%99s-formula-rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c12-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-%e2%80%8cexercise%e2%80%8c-%e2%80%8c121-%e2%80%8csolutions\" title=\"Examples of Heron\u2019s Formula RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c12 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c \u200cExercise\u200c \u200c12.1 \u200cSolutions\">Examples of Heron\u2019s Formula RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c12 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c \u200cExercise\u200c \u200c12.1 \u200cSolutions<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c12-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-%e2%80%8cexercise%e2%80%8c-%e2%80%8c12-1-%e2%80%8csolutio\/#frequently-asked-questions-faqs-of-rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c12-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-%e2%80%8cexercise%e2%80%8c-%e2%80%8c121-%e2%80%8csolutions%e2%80%8c\" title=\"Frequently Asked Questions (FAQs) of RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c12 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c \u200cExercise\u200c \u200c12.1 \u200cSolutions\u200c\">Frequently Asked Questions (FAQs) of RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c12 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c \u200cExercise\u200c \u200c12.1 \u200cSolutions\u200c<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c12-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-%e2%80%8cexercise%e2%80%8c-%e2%80%8c121-%e2%80%8csolutions%e2%80%8c-pdf\"><\/span>Download RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c12 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c \u200cExercise\u200c \u200c12.1 \u200cSolutions\u200c PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 500px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br \/><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/02\/Solutions-for-Class-9-Maths-Chapter-12-Herons-Formula-Exercise-12.1.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/02\/Solutions-for-Class-9-Maths-Chapter-12-Herons-Formula-Exercise-12.1.pdf\">Solutions for Class 9 Maths Chapter 12 Heron&#8217;s Formula Exercise 12.1<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"important-definitions-rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c12-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-%e2%80%8cexercise%e2%80%8c-%e2%80%8c121-%e2%80%8csolutions%e2%80%8c\"><\/span>Important Definitions RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c12 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c \u200cExercise\u200c \u200c12.1 \u200cSolutions\u200c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>We can calculate any triangle if we know the length of all three (3) sides of that triangle by using Heron\u2019s Formula, which has been known for approximately 2000 years. It is known as \u201cHeron\u2019s Formula\u201d after Hero of Alexandria.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"heron%e2%80%99s-formula\"><\/span><strong>Heron\u2019s Formula<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Area of a triangle= \u221as (s-a) (s-b) (s-c)<\/p>\n<p>Semi Perimeter= s=(a+b+c)2, where, a, b, and c are the sides of the triangle.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"examples-of-heron%e2%80%99s-formula-rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c12-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-%e2%80%8cexercise%e2%80%8c-%e2%80%8c121-%e2%80%8csolutions\"><\/span><strong>Examples of Heron\u2019s Formula RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c12 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c \u200cExercise\u200c \u200c12.1 \u200cSolutions<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Ques- In a triangle PQR, PQ = 15cm, QR = 13cm, and PR = 14cm. Find the area of a triangle PQR and hence its altitude on PR.<\/p>\n<p>Solution-<\/p>\n<p>Let the sides of the given triangle be PQ = p, QR = q, PR = r, respectively.<\/p>\n<p>Here,<\/p>\n<p>= p = 15 cm<\/p>\n<p>= q = 13 cm<\/p>\n<p>= r = 14 cm<\/p>\n<p>From Heron\u2019s Formula;<\/p>\n<p>Area of a triangle= \u221as (s-p) (s-q) (s-r)<\/p>\n<p>Semi Perimeter= s=(p+ q+ r)2<\/p>\n<p>Where, p, q, and r are sides of a triangle.<\/p>\n<p>= s= (15 + 13 + 14)\/ 2<\/p>\n<p>= s= 21<\/p>\n<p>= Area= \u221a21 (21-15) (21-13) (21-14)<\/p>\n<p>= \u221a21 (6 x 7 x 8)<\/p>\n<p>= \u221a7056<\/p>\n<p>= 84<\/p>\n<p>= Area = 84 cm2<\/p>\n<p>= Let, QT is a perpendicular on PR<\/p>\n<p>Now, area of triangle = \u00bd x Base x Height<\/p>\n<p>= \u00bd \u00d7 QT \u00d7 PR = 84<\/p>\n<p>= QT = 12cm<\/p>\n<p>= The altitude is 12 cm (Hence Proved).<\/p>\n<h2><span class=\"ez-toc-section\" id=\"frequently-asked-questions-faqs-of-rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c12-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-%e2%80%8cexercise%e2%80%8c-%e2%80%8c121-%e2%80%8csolutions%e2%80%8c\"><\/span>Frequently Asked Questions (FAQs) of RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c12 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c \u200cExercise\u200c \u200c12.1 \u200cSolutions\u200c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Ques-\u00a0What is S in a Triangle of Hero\u2019s Formula?<\/p>\n<p>Ans- The other is Heron\u2019s formula, which gives the area in terms of the three sides of a triangle, specifically, as the square root of the product s(s \u2013 a)(s \u2013 b)(s \u2013 c), where, \u2018s\u2019 is the semi perimeter of a triangle. So, s = (a + b + c)\/2.<\/p>\n<p><strong>Ques- What is the semi perimeter of a triangle?<\/strong><\/p>\n<p><strong>Ans-<\/strong> A semi perimeter of a triangle is equivalent to the perimeter of its medial triangle.<\/p>\n<p>Ques-\u00a0Who gave Heron\u2019s formula?<\/p>\n<p>Ans- Hero of Alexandria, a great mathematician who derived the formula to calculate the area of the triangle using the length of all three (3) sides.<\/p>\n<p><a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Know about CBSE Board<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c12 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c \u200cExercise\u200c \u200c12.1 \u200cSolutions\u200c is concerned with Heron\u2019s formula. The students will study \u201chow to find the area of a triangle using heron\u2019s formula?\u201d with the help of several solved problems. The experts have used the step-by-step problem-solving methods of the examples mentioned in this article. Students can freely &#8230; <a title=\"RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c12 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c \u200cExercise\u200c \u200c12.1 \u200cSolutions\u200c\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd%e2%80%8c-%e2%80%8csharma%e2%80%8c-%e2%80%8cchapter%e2%80%8c-%e2%80%8c12-%e2%80%8cclass%e2%80%8c-%e2%80%8c9%e2%80%8c-%e2%80%8cmaths%e2%80%8c-%e2%80%8cexercise%e2%80%8c-%e2%80%8c12-1-%e2%80%8csolutio\/\" aria-label=\"More on RD\u200c \u200cSharma\u200c \u200cChapter\u200c \u200c12 \u200cClass\u200c \u200c9\u200c \u200cMaths\u200c \u200cExercise\u200c \u200c12.1 \u200cSolutions\u200c\">Read more<\/a><\/p>\n","protected":false},"author":241,"featured_media":72865,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2985,2917,73719,73411,73410],"tags":[3081,3086,3085],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/72864"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/241"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=72864"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/72864\/revisions"}],"predecessor-version":[{"id":73797,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/72864\/revisions\/73797"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/72865"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=72864"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=72864"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=72864"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}