एक त्रिभुज जिसके शीर्ष (2, 4), (-3, -1) और (5, 3) हैं, उसका क्षेत्रफल कितना है?

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RRB ALP Previous Paper 11 (Held On: 17 Aug 2018 Shift 1)
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  1. 7 वर्ग इकाई
  2. 14 वर्ग इकाई
  3. 20 वर्ग इकाई
  4. 10 वर्ग इकाई

Answer (Detailed Solution Below)

Option 4 : 10 वर्ग इकाई
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Detailed Solution

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दिया गया है: 

(x1 ,y1) =  (2, 4),

(x2,y2) = (-3, -1) 

(x3 ,y3)= (5, 3)

प्रयुक्त सूत्र:

त्रिभुज का क्षेत्रफल = [x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)]/2

गणना:

त्रिभुज का क्षेत्रफल = [x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)]/2

सूत्र में मानों को प्रतिस्थापित करने पर,

⇒ [2(-1 – 3) + (-3)(3 – 4) + 5(4 + 1)]/2

⇒ [-8 + 3 + 25]/2 = 10 वर्ग ईकाई

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