∆ACD:
Since each side has a length of 3, ∆ACD is equilateral.
Area of an equilateral triangle = (s²/4)√3.
Thus, the area of ∆ACD = (3²/4)√3 = (9/4)√3.
∆ABE:
∆ABE is a 30-60-90 triangle.
In a 30-60-90 triangle, the sides are in the following ratio:
1 - √3 - 2.
Since AB=1, BE=√3, as shown in the figure above.
Thus, the area of ∆ABE = (1/2)bh = (1/2)(AB)(BE) = (1/2)(1)(√3) = (√3)/2.
BCDE:
∆ACD - ∆ABE = (9/4)√3 - (√3)/2 = (9/4)√3 - (2/4)√3 = (7/4)√3.
The correct answer is
B.
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