正五邊形題目求面積

2014-11-13 7:41 am
題目:

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ans: 5√3/4 - π/6

回答 (1)

2014-11-14 4:31 am
✔ 最佳答案


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曲邊形MPN = 2 × 扇形MNP - △MNP
A + 3B + 2C + S = 2 × π/6 - ½ sin60° = π/3 - √3/4 ... ①扇形MNOP = (108°/360°)π
2A + 4B + 3C + S = 3π/10 ... ② 5 × (② - ①) :
5(2A + 4B + 3C + S - A - 3B - 2C - S) = 5(3π/10 - π/3 + √3/4)
5A + 5B + 5C = 5(√3/4 - π/30)
剩下的面積 = 5√3/4 - π/6


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