Question
Download Solution PDFशीर्ष (1, -2), (3, 1) और (2, 4) के साथ त्रिभुज का क्षेत्रफल ज्ञात करें।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
बिंदु (x1, y1), (x2, y2) और (x3, y3) के साथ त्रिभुज का क्षेत्रफल = \(\rm {1\over2}\begin{vmatrix} \rm x_1 & \rm y_1 & 1\\ \rm x_2 & \rm y_2& 1\\ \rm x_3 & \rm y_3 & 1 \end{vmatrix}\)
गणना
त्रिभुज का क्षेत्रफल A = \(\rm {1\over2}\begin{vmatrix} \rm x_1 & \rm y_1 & 1\\ \rm x_2 & \rm y_2& 1\\ \rm x_3 & \rm y_3 & 1 \end{vmatrix}\)
⇒ A = \({1\over2}\begin{vmatrix} 1 &-2 & 1\\ 3& 1& 1\\ 2 & 4 & 1 \end{vmatrix}\)
⇒ 2A = 1(1 - 4) - (-2)(3 - 2) + 1(12 - 2)
⇒ 2A = -3 + 2 + 10
⇒ A = \(9\over2\) = 4.5 वर्ग इकाई
Last updated on Jul 11, 2025
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