Example 6 - Sanya has a piece of land which is in shape - Finding area of quadrilateral

  1. Chapter 12 Class 9 Herons Formula
  2. Serial order wise

Transcript

Example 6 Sanya has a piece of land which is in the shape of a rhombus She wants her one daughter and one son to work on the land and produce different crops. She divided the land in two equal parts. If the perimeter of the land is 400 m and one of the diagonals is 160 m, how much area each of them will get for their crops? Let the piece of land be ABCD It is Given that Diagonal = 160 m BD = 160 m. Also, Perimeter = 400 m AB + BC + CD + AD = 400 m ๐‘ฅ + ๐‘ฅ + ๐‘ฅ + ๐‘ฅ = 400 m 4x = 400 Now we have to find Area each will get, i.e. Area of ฮ” ADB & ฮ” BCD For ฮ”ABD , Area of triangle = โˆš(s(sโˆ’a)(sโˆ’b)(s โˆ’c)) Here, s is the semi-perimeter, and a, b, c are the sides of the triangle Here, a= 100 m , b = 100 m , c = 160 m Area of ฮ” ABD =โˆš(๐‘ (๐‘  โˆ’๐‘Ž)(๐‘  โˆ’๐‘)(๐‘  โˆ’๐‘)) Putting a= 100 m , b = 100 m , c = 160 m ,s = 180 m = โˆš(180(180 โˆ’100)(180 โˆ’100)(180 โˆ’160)) = โˆš(180ร—80ร—80ร—20) m2 = โˆš((18ร—8ร—8ร—2)ร—(10)4) m2 = โˆš(36ร—(8ร—8)ร—(10)4) = โˆš(62ร—(82)ร—(10)4) = โˆš((6)2) ร— โˆš((82) ) ร— โˆš((104) ) = 6 ร— 8 ร— ใ€–(104)ใ€—^(1/2) = 6 ร— 8 ร— 102 = 6 ร— 8 ร— 100 = 4800 m2 Thus, Area ฮ”ABD = 4800 m2 Similarly, Area ฮ”BCD = 4800 m2 Thus, Area of son = 4800 m2 and Area of daughter = 4800 m2.

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.