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Ex 12.2, 9 - A field is in the shape of a trapezium whose - Finding area of quadrilateral

 

  1. Chapter 12 Class 9 Herons Formula
  2. Serial order wise
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Ex 12.2, 9 A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field. Area of trapezium = 1/2 × Sum of parallel sides × Height = 1/2 × (AB + DC) × BF To calculate BF, we do the following steps Step 1: Draw BE ∥ AD Note AB ∥ DE Since, opposite sides are parallel, ABED is a parallelogram In parallelogram, opposite sides are equal ∴ BE = AD = 13 m & ED = AB = 10 m Also, EC = DC − ED = 25 – 10 = 15 m Finding Area Δ BEC by Herons formula Area Δ BEC 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 = 14 m , b = 15m, c = 13 m s = (𝑎 + 𝑏 + 𝑐)/2 Area of ΔBEC = √(𝑠(𝑠 −𝑎)(𝑠 −𝑏)(𝑠 −𝑐)) Putting a = 14 m , b = 15m, c = 13 m & s = 21 m = √(21(21 −13)(21 −14)(21 −15))m2 = √(21(8)(7)(6)) = √((7×3)×(8)×(7)×(2×3)) = √((7×7)×(8×2)×(3×3)) = √((7×7)×(16)×(3×3)) = √((72)×(42)×(32)) = √((7)2) × √((4)2) × √((3)2) = 7× 4 × 3 = 84 m2 Since ΔBEC has height BF and base EC, we use base height formula to find area Area of ΔBEC  = 1/2 × Base × Height Area of ΔBEC  = 1/2 × CE × BF 84 m2 = 1/2 × 15 m × BF BF = 84 × (2/15) m BF = 11.2 m Area of trapezium = 1/2 × Sum of parallel sides × Height = 1/2 × (AB + DC) × BF = 1/2 × (10 + 25) × 11.2 = 1/2 × (35) × 11.2 = 196 m2

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