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Ex 12.2, 8 - A floral design on a floor is made up of - Finding area of quadrilateral

  1. Chapter 12 Class 9 Herons Formula
  2. Serial order wise
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Ex 12.2, 8 A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm and 35 cm (see the given figure). Find the cost of polishing the tiles at the rate of 50p per cm2. There are total 16 tiles , in shape of triangle Area of tiles = 16 × Area of 1 triangle Area of triangle 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 = 9cm , b = 28cm, c =35cm s = (𝑎 + 𝑏 + 𝑐)/2 Area of triangle = √(𝑠(𝑠 −𝑎)(𝑠 −𝑏)(𝑠 −𝑐)) Putting a = 9, b = 28 , c = 35 & s = 36 = √(36(36−9)(36−28)(36−35)) = √(36" ×" (27) "× " (8)" × " (1)) = √(36" ×" (9" × " 3) "×" (4" × " 2)) = √((36)" ×" (9)" × (4" ) "×" (3)" × (" 2)) = √((62)" ×" (32)" × (22" ) "×" (3)" × (" 2)) = √62 ×√32 ×√22 ×√(3×2) = 6× 3 × 2 √((6) ) = 36√6 cm2 = 36 × 2.45 cm2 = 88.2 cm2 Area of tiles = 16 × Area of 1 triangle ∆ABC = (16 × 88.2) cm2 = 1411.2 cm2 Cost of polishing per cm2 area = 50 p Cost of polishing 1411.2 cm2 area = Rs (1411.2 × 1/2) = Rs 705.60 Therefore, it will cost ₹ 705.60 while polishing all the tiles.

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