×

Hello! Socratic's Terms of Service and Privacy Policy have been updated, which will be automatically effective on October 6, 2018. Please contact hello@socratic.com with any questions.

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

1 Answer
Jun 5, 2017

Answer:

Area #=3sqrt3 " m"^2#

Explanation:

enter image source here

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#