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    Question

    If the perimeter of a rhombus is 2p units and the sum of

    the diagonals is m units, then find the area of the rhombus?
    A (p²-m²)/4 square unit Correct Answer Incorrect Answer
    B (m²-p²)/4 square unit Correct Answer Incorrect Answer
    C (m²-p²)/2 square unit Correct Answer Incorrect Answer
    D p²/2 square unit Correct Answer Incorrect Answer

    Solution

    The perimeter of a rhombus =2p Side =p/2 AC= 2a, BD=2b OB =OD=b In ΔAOB- p²/4 = a² + b² p² =4a²+4b²… (1) m² =(2a+2b) ² m²= 4a²+4b²+8ab  m²-8ab =4a²+4b² m²-8ab=p² m²-p²=8abdivided by 4 ¼ (m²-p²) =2ab…. (2) Area 0f rhombus=d₁×d₂/2  = 2a×2b/2 =2ab   from equation (2)  =m²-p²/4 square unit

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