{"id":25956,"date":"2021-06-24T15:47:36","date_gmt":"2021-06-24T10:17:36","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=25956"},"modified":"2022-03-02T10:47:36","modified_gmt":"2022-03-02T05:17:36","slug":"ncert-solutions-for-class-9-maths-chapter-12-ex-12-1","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-12-ex-12-1\/","title":{"rendered":"NCERT Solutions for Class 9 Maths Chapter 12 Heron\u2019s Formula Ex 12.1"},"content":{"rendered":"

These NCERT Solutions for Class 9 Maths<\/a> Chapter 12 Heron\u2019s Formula Ex 12.1 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 9 Maths Chapter 12 Heron\u2019s Formula Exercise 12.1<\/h2>\n

Question 1.
\nA traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using the Herons formula. If its perimeter is 180 cm, what will be the area of the signal board?
\nSolution:
\nIn first case, length of each sides of an equilateral triangle is a
\ns = \\(\\frac{a+b+c}{2}=\\frac{3 a}{2}\\)
\nTherefore by Heron\u2019s formula-
\n\"NCERT
\nor, area of triangle = \\(\\frac{\\sqrt{3} \\cdot a^{2}}{4}\\)
\nIn case II,
\nPerimeter of an equilateral triange is 180 cm
\n\u2234 One side = \\(\\frac{180}{3}\\) = 60 cm
\ns = \\(\\frac{60+60+60}{2}\\) = 90 cm.
\n\u2234 Area of signal board = \\(\\sqrt{s(s-a)(s-b)(s-c)}\\)
\n= \\(\\sqrt{90(90-60)(90-60)(90-60)}\\)
\n= \\(\\sqrt{90 \\times 30 \\times 30 \\times 30}\\)
\n= 900\u221a3 cm2<\/sup>
\nor, Area of signal board = 900\u221a3 cm2<\/sup>.<\/p>\n

\"NCERT<\/p>\n

Question 2.
\nThe triangular side walls of a flyover have been used for advertisements. The sides of the wall are 122 m, 22 m, and 120 m (see fig. 12.9). The advertisements yield an earning of Rs. 5000 per m2<\/sup> per year. A company hired one of its walls for 3 months. How much rent did it pay?
\n\"NCERT
\nSolution:
\nThe sides of the triangular wall are 122 m, 22 m, and 120 m.
\n\u2234 s = \\(\\frac{120+22+120}{2}\\) = 132 m.
\nTherefore, by Heron’s Formula.
\nArea of triangular wall
\n= \\(\\sqrt{132(132-122)(132-122)(132-122)}\\)
\n= \\(\\sqrt{132 \\times 10 \\times 110 \\times 12}\\)
\n= 1320 m2<\/sup>
\n\u2234 Rent = 5000 \u00d7 1320 \u00d7 \\(\\frac{3}{12}\\) = 16,50,000
\nTherefore, rent of this wall for 3 months is Rs. 16,50,000<\/p>\n

\"NCERT<\/p>\n

Question 3.
\nThere is a slide in a park. One of its side walls has been painted in some colour with a message \u201cKEEP THE PARK GREEN AND CLEAN\u201d (see Fig. 12.10 ). If the sides of the wall are 15m, 11m, and 6m, find the area painted in colour.
\n\"NCERT
\nSolution:
\nThe sides of the wall are 15 m, 11 m, and 6 m.
\n\u2234 s = \\(\\frac{15+11+6}{2}\\) = 16 m
\n\u2234 By Heron’s formula, we know that
\nArea of the wall
\n\"NCERT
\nTherefore, the Area of the wall is 20\u221a2 m2<\/sup>.<\/p>\n

\"NCERT<\/p>\n

Question 4.
\nFind the area of the triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.
\nSolution:
\nLet third side of triangle is x cm.
\n\u2234 Perimeter = 18 + 10 + x
\n\u21d2 42 = 18 + 10 + x
\n\u21d2 x = 14 cm
\ns = \\(\\frac{18+10+14}{2}=\\frac{42}{2}\\) = 21
\nBy Heron’s formula we know that
\nArea of triangle
\n\"NCERT
\nTherefore, the area of the triangle = 2\u221a11 cm2<\/sup>.<\/p>\n

\"NCERT<\/p>\n

Question 5.
\nSides of triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.
\nSolution:
\nLet the first side of triangle = 12x
\nSecond side of triangle = 17x
\nand third side of triangle = 25x
\nTherefore,
\nperimeter of triangle = 12x + 17x + 25x
\n\u21d2 540 = 54x
\n\u21d2 x = 10
\nFirst side of triangle = 12x = 12 \u00d7 10 = 120 cm
\nSecond side of triangle = 17x = 17 \u00d7 10 = 170 cm
\nand Third side of triangle = 25x = 25 \u00d7 10 = 250 cm
\n\u2234 s = \\(\\frac{120+170+250}{2}=\\frac{540}{2}\\) = 270
\n\u2234 By Heron’s formula we know that
\nArea of triangle
\n\"NCERT
\nTherefore, area of triangle = 9000 cm2<\/sup><\/p>\n

\"NCERT<\/p>\n

Question 6.
\nAn isosceles triangle has a perimeter of 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
\nSolution:
\nLet the third side of an isosceles triangle is x.
\n\u2234 Perimeter of triangle = 12 + 12 + x
\nor, 30 = 24 + x
\nor, x = 6x m.
\nThe third side of an isosceles triangle is 6 cm.
\n\u2234 s = \\(\\frac{12+12+6}{2}\\) = 15
\nBy Heron’s formula, we know that
\nArea of triangle
\n\"NCERT
\nTherefore, the area of an isosceles triangle is 9\u221a15 cm2<\/sup>.<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 9 Maths Chapter 12 Heron\u2019s Formula Ex 12.1 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 9 Maths Chapter 12 Heron\u2019s Formula Exercise 12.1 Question 1. A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area …<\/p>\n

NCERT Solutions for Class 9 Maths Chapter 12 Heron\u2019s Formula Ex 12.1<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[6],"tags":[],"yoast_head":"\nNCERT Solutions for Class 9 Maths Chapter 12 Heron\u2019s Formula Ex 12.1 - MCQ Questions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-12-ex-12-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 9 Maths Chapter 12 Heron\u2019s Formula Ex 12.1 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 9 Maths Chapter 12 Heron\u2019s Formula Ex 12.1 Questions and Answers are prepared by our highly skilled subject experts. 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