F.2 Math area~

穎霖

2008-05-16 3:22 am

In the figure,ABC is an equilateral triangle of sides 8 cm.Find the length of the curve which is composed of arcs of radius 2 cm
http://s194.photobucket.com/albums/z30/skywalker_handsome/?action=view&current=DSC00241.jpg

The figure shows a square ABCD of sides 4 cm.B and D are the centres of the two arcs.Find the shaded area
http://i194.photobucket.com/albums/z30/skywalker_handsome/DSC00242.jpg

更新1:

correct to 3 significant figure

更新2:

我想問點知果個semi circle既直徑係4 cm????我比較遲純?

回答 (1)

cliffordchow1225

2008-05-16 2:48 pm

✔ 最佳答案

1) the whole curve is formed by 3 semi-circle and 3 60-degree arc (equilateral triangle)
It is given that the radius of semi-circle is 4, therefore length of them:
= 3(2 x 2 x 3.14 x 1/2)
= 18.84 (cm)

Radius of the 60-degree arc = [8 - (2 x 2)]/2 = 2 (cm)
length of the 3 60-degree arc:
= 3(2 x 2 x 3.14 x 1/6)
= 6.28 (cm)

Length of the whole curve
= 18.84 + 6.28
= 25.12 (cm)

2) Firstly, draw a line AC.
the area of the unshaped part
= 2[arc ABC - triangle ABC]
= 2[(4^2 x 3.14 x 1/4) - (4 x 4 x 1/2)]
= 2(12.52 - 8)
= 9.04 (cm^2)

Shaped area = square ABCD - unshaped area
= (4 x 4) - 9.04
= 16-9.04
= 6.96 (cm^2)

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