Sanya has a piece of land which is in the shape of a rhombus. -Maths 9th

Sanya has a piece of land which is in the shape of a rhombus. -Maths 9th
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Let ABCD be the field. Given perimeter = 400 m So, each side = 400/4 = 100 m Diagonal BD = 160 m Let a = 100 m, b = 100 m, c = 160 m ∴ s = (a + b + c)/2  = (100 + 100 + 160)/2 = 180 m. Therefore,    Area of △ABD = root under ( √s(s - a)(s - b)(s - c))  = root under (√180(180 - 100)(180 - 100)(180 - 160))  = root under (√180 x 80 x 80 x 20) = 4800 m2 Alternative method: As the diagonals of rhombus bisect each other: Therefore OD = 1/2.BD = 1/2 x 160 = 80 m OC =  1/2.AC  In △OCD, we have, CD2 = OC2 + OD2  1002  =  OC 2  + 802    ⇒  OC2 = 10000 - 6400  ⇒ OC2  = 3600  ⇒ OC = 60 m Therefore, area of △BCD = 1/2(BD x OC) = 1/2 x 160 x 60 = 4800 m2  ∴  Each of them will get 4800 m2 of area for their crops.
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