Question
Download Solution PDF(7, 3), (10, 0) এবং (0, -4) স্থানাঙ্ক দ্বারা গঠিত ত্রিভুজের ক্ষেত্রফল নির্ণয় করুন।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFপ্রদত্ত:
ত্রিভুজের স্থানাঙ্ক (7, 3), (10, 0) এবং (0, -4)
অনুসৃত সূত্র:
ত্রিভুজের ক্ষেত্রফল = (1/2) × |{Ax(By - Cy)} + {Bx(Cy - Ay)} + {Cx(Ay - By)}| বর্গ একক
এখানে, Ax এবং Ay হল A এর শীর্ষবিন্দুতে x এবং y স্থানাঙ্ক।
একই শর্ত B এবং C শীর্ষবিন্দুর x এবং y স্থানাঙ্কে প্রযোজ্য।
গণনা:
এখানে, Ax = 7 এবং Ay = 3
Bx = 10 এবং By = 0
এবং, Cx = 0 এবং Cy = -4
সূত্র অনুযায়ী,
ত্রিভুজের ক্ষেত্রফল = (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| বর্গ একক
⇒ (1/2) × |28 - 70|
⇒ (1/2) × 42
⇒ 21 বর্গ একক
∴ ত্রিভুজের ক্ষেত্রফল 21 বর্গ একক।
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