Question
Download Solution PDFनिर्देशांकों (7, 3), (10, 0) और (0, -4) से बनने वाले त्रिभुज का क्षेत्रफल ज्ञात कीजिये।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया है:
त्रिभुज के निर्देशांक (7, 3), (10, 0) और (0, -4) हैं।
प्रयुक्त सूत्र:
त्रिभुज का क्षेत्रफल = (1/2) × |Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)|वर्ग इकाई
यहाँ, शीर्ष A के x और y निर्देशांक Ax और Ay हैं।
B और C शीर्षों के x और y अंकन के लिए समान अवधारणा लागू होती है।
गणना:
यहाँ, Ax = 7 और Ay = 3
Bx = 10 और By = 0
और, Cx = 0 और Cy = -4
सूत्र के अनुसार हमें प्राप्त होता है,
त्रिभुज का क्षेत्रफल = (1/2) × |Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)
⇒ (1/2) × |{7 × (0 - (-4))} + {10 × ((-4) - 3)} + {0 × (3 - 0)}|
⇒ (1/2) × |7(4) + 10(-7) + 0| वर्ग इकाई
⇒ (1/2) × |28 - 70|
⇒ (1/2) × 42
⇒ 21 वर्ग इकाई
∴ त्रिभुज का क्षेत्रफल 21 वर्ग इकाई है।
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