between PR and QS, show that the area of the quadrilateral PQRS is
1/2 QS x PR sinθ.
更新1:
我想問 SIN θ在那裡?
MATHS 數學 的圖形, 證明題
2008-04-14 5:47 am
PR and QS are the diagonals of the quadrilateral PQRS. Ifθis the acute angle
between PR and QS, show that the area of the quadrilateral PQRS is
1/2 QS x PR sinθ.
between PR and QS, show that the area of the quadrilateral PQRS is
1/2 QS x PR sinθ.
回答 (1)
2008-04-14 5:56 am
✔ 最佳答案
Let X be the pt of the intersection of PR and QSArea of PQRS
= 1/2 (QX)(PX)sinθ+1/2 (RX)(SX) sinθ+1/2(QX)(RX)sinθ+1/2(PX)(SX)sinθ
=1/2sinθ(QXPX+RXSX+QXRX+PXSX)
=1/2sinθ(QX(PX+RX)+SX(PX+RX))
=1/2sinθ(QX+SX)(PX+SX)
=1/2 QS x PR sinθ
收錄日期: 2021-05-03 04:39:54
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