第 23 題
易知 AC = 12
作 AE 垂直 BC 於 E，AF 垂直直線 CD 於 F
△AEC 和 △AFC 全等

AF = AE = 60/13
CF = CE = 144/13
DF = 25/13
CD = 119/13

ABCD = △ABC + △ADC = 5 * 12 * (1/2) + (119/13) * (60/13) * (1/2) = 8640/169

第 24 題
作 EP 垂直 AD 於 P，FQ 垂直 AD 於 Q
則 AP = PQ = QD = (2/3)√3，EP = 2/3，FQ = 4/3

PG/DG = EP/BD = 1/3
PG = (1/4)DP = (1/3)√3
AG = √3

QH/DH = FQ/BD = 2/3
DH = (3/5)QD = (2/5)√3

AG：GH：DH = 5：3：2

△BGH = (3/10)△ABD = (3/20)△ABC
EFHG = (1/3)△ABC - (3/20)△ABC = (11/60)△ABC = (11/15)√3


國中的方法，不簡單啊 ......

第 21 題
∠DAF + ∠BAE = ∠EAG + ∠GAF = 45 度
又 ∠BAE = ∠EAG
故 ∠DAF = ∠GAF
又 AD = AB = AG
△ADF 和 △AGF 全等 (SAS)

DF = GF = 3
令 AG = x
在 △CEF 中，CE^2 + CF^2 = EF^2
(x - 5)^2 + (x - 3)^2 = (5 + 3)^2
x = 4 + √31

△AEF = 4x = 16 + 4√31