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106復興高中

7 另解

\(\Delta ABQ \sim \Delta PRQ\)
\(\Delta APQ \sim \Delta BRQ\)
又\(\overline{PQ} = \overline{BQ} = \sqrt{2} \),\(\overline{AQ} = \sqrt{10} \)
所以\(\overline{PQ} : \overline{AQ} = \overline{BQ} : \overline{AQ} = 1: \sqrt{5} \)
\(PABR = \Delta APQ + \Delta BQR + \Delta ABQ + \Delta PQR = \Delta APQ + \frac{1}{5} \Delta APQ + \Delta ABQ + \frac{1}{5} \Delta ABQ = \frac{6}{5} \Delta ABP = \frac{24}{5}\)

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