How doy ou find the area of an equilateral triangle inscribed in a circle with a circumference of 64(pi) cm?

1 Answer
Alan P.
Jun 1, 2015

If the circumference of a circle is #64pi# cm. then it's diameter is #64# cm. (since circumference #= 2 * #diameter).

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Based on the diagram (above).

The sides of this equilateral triangle have a length of
#s=cos(30^@)*64#
#color(white)("XXXXX")#and since #cos(30^@) = sqrt(3)/2#
#= 32sqrt(3)#

The height of the equilateral triangle is
#h = cos(30^@) * s#

#= sqrt(3)/2* 32sqrt(3)#

#=48#

The area of the equilateral triangle is
#A= 1/2sh#

#= 1/2*32sqrt(3)*48#

#=768sqrt(3)#

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