有關4個1/4圓

2008-11-07 5:53 am
http://d.imagehost.org/0600/p10589.jpg
正方形邊長10cm,求中間間條部份。
要公式+答案,步驟同解釋可免。唔該

回答 (3)

2008-11-07 3:15 pm
✔ 最佳答案
Area of sector = pr^2(angle)/360 where p = pi.
= p(10)^2(30/360) = 25p/3.
Area of triangle = (1/2)absinC = (1/2)(10)(10)sin30 = 25.
So area of minor segment = 25p/3 - 25 = 25(p-3)/3.
Area of 4 minor segments = 100(p-3)/3.........................(1)
Using cosine rule, area of square
= (10)^2 + (10)^2 - 2(10)(10)cos30 = 200 - 200(sqrt3)/2 = 200(2-sqrt3)/2
= 100(2 - sqrt3) .....................(2)
So area of shaded region = (1) + (2)
= 100[(p-3)/3 + 2 - sqrt3].
=31.5 cm^2.
2008-11-10 12:21 am
pr^2(angle)/360 where p = pi.

=31.5cm^2
參考: cc7
2008-11-07 7:57 am
計係計到,不過有D複雜,諗緊個簡單D既方法。


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