প্রদত্ত একটি রম্বসের প্রতিটি বাহুর দৈর্ঘ্য 5 মিটার করে এবং তার একটি কর্ণের দৈর্ঘ্য 2.8 মিটার। তাহলে রম্বসটির ক্ষেত্রফল কত হবে?

This question was previously asked in
RRC Group D Previous Paper 24 (Held On: 20 Sept 2018 Shift 2)
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  1. 7 মিটার2
  2. 13.44 মিটার2
  3. 6.72 মিটার2
  4. 14 মিটার2

Answer (Detailed Solution Below)

Option 2 : 13.44 মিটার2
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Detailed Solution

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ধরি, রম্বসটির অপর কর্ণের দৈর্ঘ্য 2x মিটার

আমরা জানি,

a2 = (d1/2)2 + (d2/2)2           [a =রম্বসের বাহু , d1 এবং d2 হ'ল কর্ণদ্বয়ের দৈর্ঘ্য]

⇒ (2.8/2)2 + (2x/2)2 = (5)2

⇒ 1.96 + x2 = 25

⇒ x2 = 23.04

⇒ x = 4.8 মিটার

অপর কর্ণের দৈর্ঘ্য = 4.8 × 2 = 9.6 মিটার

আর, রম্বসটির ক্ষেত্রফল হ'ল = ½ × কর্ণের গুণফল

∴ রম্বসটির ক্ষেত্রফল = 1/2 × 2.8 × 9.6 = 13.44 মিটার2
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