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Ex 12.2, 5 - A rhombus shaped field has green grass - Finding area of quadrilateral

  1. Chapter 12 Class 9 Herons Formula
  2. Serial order wise
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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 Δ ABD + Area Δ BCD Finding area Δ ABD For ΔABD , 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 Δ ABD = √(𝑠(𝑠 −𝑎)(𝑠 −𝑏)(𝑠 −𝑐)) 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 ΔABD = 432 m2 Similarly, Area Δ BCD = 432 m2 So, Area of rhombus ABCD = Area Δ ABD + Area Δ 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 = (𝐴𝑟𝑒𝑎 𝑜𝑓 𝑟ℎ𝑜𝑚𝑏𝑢𝑠 )/18 = 864/18 = 48 m2 Thus, Each cow will get 48 m2 area of grass field.

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