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How do you find the area of an equilateral triangle with an apothem of #4sqrt3#?

1 Answer

Dec 7, 2015

#144sqrt3#

Explanation:

enter image source here

(source: wolfram.com)

#color(white)(xx)tan30=sqrt3/3#

#=>(4sqrt3)/(a/2)=sqrt3/3#
#=>color(red)((a/2)*2*1/sqrt3*3)(4sqrt3)/(a/2)=color(red)((a/2)*2*1/sqrt3*3)sqrt3/3#
#=>a=24#

#A=1/4sqrt3*24^2#
#color(white)(xx)=144sqrt3#

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