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?Solution
The perimeter of a rhombus =2p Side =p/2 AC= 2a, BD=2b OB =OD=b In ĪAOB- pĀ²/4 = aĀ² + bĀ² pĀ² =4aĀ²+4bĀ²ā¦ (1) mĀ² =(2a+2b) Ā² mĀ²= 4aĀ²+4bĀ²+8abĀ mĀ²-8ab =4aĀ²+4bĀ² mĀ²-8ab=pĀ² mĀ²-pĀ²=8abdivided by 4 Ā¼ (mĀ²-pĀ²) =2abā¦. (2) Area 0f rhombus=dāĆdā/2 Ā = 2aĆ2b/2 =2abĀ Ā from equation (2) Ā =mĀ²-pĀ²/4 square unit 
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