Question
Download Solution PDFउस चतुर्भुज का क्षेत्रफल ज्ञात कीजिए जिसके शीर्ष A (0, 0), B (0, 10), C (8, 2) और D (8, 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 हुआ: A (0, 0), B (0, 10), C (8, 2) और D (8, 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 (0, 0), B (0, 10), C (8, 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 क्षेत्रफल = \(\frac{1}{2} \cdot \left| {\begin{array}{*{20}{c}} {{0}}&{{0}}&1\\ {{0}}&{{10}}&1\\ {{8}}&{{2}}&1 \end{array}} \right|\)
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