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Example 6 - Sanya has a piece of land which is in shape - Examples

  1. Chapter 12 Class 9 Herons Formula
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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 provides courses for Mathematics from Class 9 to 12. You can ask questions here.
  • Dharambir Sharma's image
    Dharambir Sharma
    May 22, 2017, 12:16 p.m.
    The sides of a quadrilateral ABCD are 6cm,8cm,12cm,and14cm respectively and the angle between the first two sides is a right angle. Find its area.













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