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An equilateral triangle is inscribed in a circle with a radius of 2 meters. What is the area of this triangle?

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Jun 5, 2017

Answer:

Area #=3sqrt3 " m"^2#

Explanation:

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As shown in the figure, #DeltaABC# is an equilateral triangle inscribed in a circle centered at #O#
Given radius #r =2 m#,
#=> OM=h=rsin30=2xx1/2=1#
#BM=a/2=rcos30=2xxsqrt3/2=sqrt3#
#AM=r+h=2+1=3#
As #AM# bisects #BC, => BC=2BM=a=2sqrt3#
Area of #DeltaABC=1/2xxAMxxBC=1/2xx3xx2sqrt3=3sqrt3 " m"^2#

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