一題數學比例題

圖片參考：http://img412.imageshack.us/img412/474/dsc01667ap0.jpg


(a)
Join AD.
As ΔABC and ΔADC are of equal base (BC = DC) and common height,
　area of ΔABC = area of ΔADC.
Also, as ΔADC and ΔADE are of equal base (AC = AE) and common height,
　area of ΔADC = area of ΔADE.
So,
　area of ΔABC : area of ΔCDE = 1 : (1+1) = 1 : 2

(b)
From (a),
　area of ΔABC : area of ΔCDE = 1 : (1+1) = 1 : 2
Similarly,
　area of ΔABC : area of ΔAEF = 1 : 2　and
　area of ΔABC : area of ΔBFD = 1 : 2
So,
　area of ΔABC : area of ΔDEF = 1 : (1+2+2+2) = 1 : 7

2007-03-28 04:03:28 補充：
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