Question
Download Solution PDFयदि A (1, 2), B (3, 6), C (5, 10) और D (3, 2) एक चतुर्भुज ABCD के शीर्ष हैं तो चतुर्भुज ABCD का क्षेत्रफल ज्ञात करें।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा :
माना कि A (x1, y1), B (x2, y2) और C (x3, y3) एक Δ ABC के शीर्ष हैं, फिर Δ ABC का क्षेत्रफल = \(\frac{1}{2} \cdot \left| {\begin{array}{*{20}{c}} {{x_1}}&{{y_1}}&1\\ {{x_2}}&{{y_2}}&1\\ {{x_3}}&{{y_3}}&1 \end{array}} \right|\)
गणना:
दिया हुआ: A (1, - 2), B (3, 6), C (5, 10) और D (3, 2) एक चतुर्भुज ABCD के शीर्ष हैं
यहां, हमें चतुर्भुज ABCD के क्षेत्र को खोजना होगा
चतुर्भुज ABCD का क्षेत्रफल = ΔABC का क्षेत्रफल + ΔACD का क्षेत्रफल
ΔABC का क्षेत्रफल ज्ञात करते हैं
∵ A (1, - 2), B (3, 6), C (5, 10) ΔABC के शीर्ष हैं
जैसा कि हम जानते हैं कि, यदि (x1, y1), B (x2, y2) और C (x3, y3) एक Δ ABC के शीर्ष हैं, फिर Δ ABC का क्षेत्रफल = \(\frac{1}{2} \cdot \left| {\begin{array}{*{20}{c}} {{x_1}}&{{y_1}}&1\\ {{x_2}}&{{y_2}}&1\\ {{x_3}}&{{y_3}}&1 \end{array}} \right|\)
⇒ Δ ABC का क्षेत्रफल = \(\frac{1}{2} \cdot \left| {\begin{array}{*{20}{c}} {{1}}&{{-2}}&1\\ {{3}}&{{6}}&1\\ {{5}}&{{10}}&1 \end{array}} \right|\)
Last updated on Jul 8, 2025
->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.
->UPSC had extended the UPSC NDA 2 Registration Date till 20th June 2025.
-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.
->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.
-> The selection process for the NDA exam includes a Written Exam and SSB Interview.
-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100.
-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential.