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# [Core] 數學難題求解!!

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## 數學難題求解!!

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 life1643 中級學徒 發短消息 加為好友 當前離線 2# 大 中 小 發表於 2017-2-25 10:02 PM (第 603 天) 只看該作者 APB is a straight line AC^2+CE^2=AE^2 so, AE=32.593 PE^2+AE^2=AP^2 so, AP=8.88 AP=HC=8.88cm ans=A UID421692 帖子44 精華0 積分3 閱讀權限10 在線時間122 小時 註冊時間2016-10-16 最後登錄2017-12-23  查看詳細資料 TOP

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## 回覆 2# life1643 的帖子

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 C74112436 高級學徒 發短消息 加為好友 當前離線 5# 大 中 小 發表於 2017-2-25 11:59 PM (第 603 天) 只看該作者 one moreem46em46 UID364832 帖子413 精華0 積分37 閱讀權限20 在線時間68 小時 註冊時間2014-12-26 最後登錄2018-5-23  查看詳細資料 TOP

## Detailed explanation

equiangular ⇒ interior angle = 360°×(6-2)/6 = 120°
Extend BC and ED such that they intersect at Y.
∠CDY  = ∠DCY = 180° - 120° = 60° (adj. ∠s on st. line)
ΔCDY is an equilateral triangle, CY = DY = 2
ΔCDY ~ ΔBEY (ratio of two sides, inc. ∠)
ΔBEY is also an equilateral triangle with side length = 6 !
Similarly, denote the intersection point of AB and FE by X.
∠AFX = ∠FAX = 60°, which shows that ΔAFX is an equilateral triangle with side length = AF = 6
AF = 5
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Denote the area of an equilateral triangle with side length = x by A(x).
A(x) = 1/2 × base × height = 1/2 × x × (x√3)/2 = x²√3/4
The required area = A(6) - A(2) + A(6) - A(5) = 43√3/4