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1000PS Section 3 Qusetion 20

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Junior | Next Rank: 30 Posts
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by cindyqtran » Sat Sep 22, 2007 10:06 pm
picture is attached.
20. If each side of ΔACD above has length 3 and if AB has length 1, what is the area of region BCDE?
(A) 9/4
(B) 7/4*sqrt(3)
(C) 9/4*sqrt(3)
(D) 7/2*sqrt(3)
(E) 6 +sqrt(3)

thanks!![/quote]
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by kajcha » Sun Sep 23, 2007 2:45 pm
Triangle ACD is equilateral triangle. So, each angle is 60 degrees

AB = 1. tan 60 = root(3) = BE/AB => BE = root(3)

Area of traingle ABE = AB*BE/2 = root(3)/2 ----(1)

Area of trianle ACD = root(3)*3*3/2 ----(2)

Area of region BCDE = (2)-(1) = 7*root(3)/4
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by cindyqtran » Sun Sep 23, 2007 3:44 pm
thanks. forgot about 30-60-90 triangles/
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