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Ex 12.2, 5 - A rhombus shaped field has green grass - Ex 12.2

Ex 12.2, 5 - Chapter 12 Class 9 Herons Formula - Part 2
Ex 12.2, 5 - Chapter 12 Class 9 Herons Formula - Part 3
Ex 12.2, 5 - Chapter 12 Class 9 Herons Formula - Part 4

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Ex 12.2, 5 A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting? Let the field be ABCD It is Given that Side of rhombus = 30 m AB = BC = CD = AD = 30 m Also, Diagonal = 48 m BD = 48 m. Area of rhombus = Area ABD + Area BCD Finding area ABD For ABD , Area of triangle = (s(s a)(s b)(s c)) Here, s is the semi-perimeter, and a, b, c are the sides of the triangle Here, a = 30 m , b = 30 m , c = 48 m Area of ABD = ( ( )( )( )) Putting a = 30 m , b = 30 m , c = 48 m & s = 54 = (54(54 30)(54 30)(54 48)) = (54 (24)(24)(6) ) = ((6 9) (24 24) (6) ) = ((6 6) (9) (24 24) ) = ((6^2) (32) ( 24 ^2) ) = ((6)2) ((32) ) ((242) ) m2 = 6 3 24 = 432 m2 Hence, Area ABD = 432 m2 Similarly, Area BCD = 432 m2 So, Area of rhombus ABCD = Area ABD + Area BCD = 432 + 432 = 864 m2 Thus, Area of Rhombus = 864 m2 Given that 18 cows to graze the field. So, Area for 18 cows = Area of rhombus Area of Each Cow = ( )/18 = 864/18 = 48 m2 Thus, Each cow will get 48 m2 area of grass field.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.