In the equilateral triangle ABC, AD = DE = BE, D and E lies on the AB. If each side of the triangle (i.e., AB, BC and AC) be 6 cm, then the area of the shaded region is :
A
9cm2
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B
6√3cm2
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C
5√3cm2
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D
Noneoftheabove
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Solution
The correct option is B6√3cm2 Area of equilateral triangle ABC=√34×(6)2=9√3cm2 Area of ΔCDE=12×DE×CP =12×2×√32×6 =3√3cm2 Hence, Area of the shaded region = 9√3cm2−3√3cm2 = 6√3cm2
Alternatively, Since, AD = DE = BE => Area of shaded region = 23×√34×(6)2 = 6√3cm2