Ex 7.2, 10 - Find area of a rhombus if its vertices are - Ex 7.2

  1. Chapter 7 Class 10 Coordinate Geometry
  2. Serial order wise
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Ex 7.2 , 10 Find the area of a rhombus if its vertices are (3, 0), (4, 5), ( 1, 4) and ( 2, 1) taken in order. [Hint : Area of a rhombus = 1/2 (product of its diagonals)] Let the vertices be A(3, 0) , B(4, 5) C( 1, 4) , D( 2, 1) We know that Area of Rhombus = 1/2 (Product of diagonals) = 1/2 AC BD We need to find AC & BD using distance formula Finding AC AC = (( 2 1)2+( 2 1)2) Here, x1 = 3 , y1 = 0 x2 = 1, y2 = 4 Putting values AC = (( 1 3 )2+(4 0)2) = (( 4 )2+(4)2) = ((4 )2+(4)2) = (2(4)2) = 2 4 = 4 2 Finding BD BD = (( 2 1)2+( 2 1)2) Here, x1 = 4 y1 = 5 x2 = 2 y2 = 1 Putting values AC = (( 2 4 )2+( 1 5)2) = (( 6 )2+( 6)2) = ((6)2+(6)2) = (2(6)2) = 2 6 = 6 2 Now, Area of Rhombus = 1/2 AC BD = 1/2 4 2 6 2 = 2 2 6 2 = (2 6) ( 2 2) = (12) (2) = 24 square units Hence, Area of rhombus = 24 square units

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