Question
Download Solution PDFउस चतुर्भुज का क्षेत्रफल ज्ञात कीजिए जिसके शीर्ष A (5, 3), B (6, - 4), C (- 3, - 2) और D (- 4, 7) हैं।
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 गया: A (5, 3), B (6, - 4), C (- 3, - 2) और D (- 4, 7) 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 (5, 3), B (6, - 4), C (- 3, - 2) 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 क्षेत्र = \(\frac{1}{2} \cdot \left| {\begin{array}{*{20}{c}} {{5}}&{{3}}&1\\ {{6}}&{{-4}}&1\\ {{-3}}&{{-2}}&1 \end{array}} \right|\)
Last updated on May 31, 2025
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