數學知識交流---面積難題(四邊形Part3)

該兩條未知邊平行的ASAAS四邊形對於所有ASAAS四邊形來說只是屬於非常特殊的個案，不應該因為該兩條未知邊平行的ASAAS四邊形有無限多個可能性而武斷地作出「ASAAS四邊形不能計算面積」這個結論。

其實縱使例如SASAS四邊形都會有機會出現「該四邊形不成立」的情況，只要該兩個已知角的和小於180度且最外圍的兩個已知邊太長就會有機會發生，難度我們為了這少許的「該四邊形不成立」的情況而放棄對該種四邊形的深入分析？

2011-09-01 23:04:16 補充：
我仍未研究到ASAAS四邊形該如何計算，事實上這是最複雜品種的四邊形。

2011-09-06 20:00:21 補充：
CRebecca，其實你的回答的case 2嚴格上仍有些問題：
1. O點有可能在EH那邊或是在FG那邊。
2. 其實就算EF與GH不平行，這仍是有機會出現令四邊形不成立的邊長內角組合，縱使其內角組合合理。請問有甚麼辦法可以檢驗出來？

2011-09-16 07:19:54 補充：

圖片參考：http://i212.photobucket.com/albums/cc82/doraemonpaul/yahooknowledge/trigonometry/areaofquadrilateral9.jpg

參考資料：
my wisdom of maths + formula from http://en.wikipedia.org/wiki/Triangle#Using_trigonometry

It can be solved uniquely.

2011-09-01 16:50:56 補充：
except 2 sides are parallel and given the length of the other 2 sides.
Jason 's answer is wrong, since the order of the four angles are different.

2011-09-02 21:23:09 補充：
再看不懂,我要刪答了!

is it called 'can not calculate the area' if there are 2 value of area comes out??
[with same sets of length of sides and angles]

2011-09-01 16:20:07 補充：

圖片參考：http://imgcld.yimg.com/8/n/HA00016323/o/701109010042313873452350.jpg

___________________________________________________________

2011-09-01 19:02:06 補充：
no one said that they must be in order.

2011-09-02 14:13:35 補充：
There are many many very difficult maths Q in the world...

I'm glad that there are many pros in yahoo knowledge to solve the very hard maths Q.

^_^

2011-09-02 19:46:18 補充：
lop,y do u cancel the ans?
'2 mathematics Q. (20pt!!)'

If there are 2 value of area comes out , it is called 'can not calculate the area' .

2011-09-01 20:50:21 補充：
doraemonpaul ,

那你不如去試試？

2011-09-16 18:02:49 補充：
Sorry for forgetting choosing the answer .