The altitude of an equilateral triangle is sqrt(6)units. What is the area of the triangle, in square units? Express your answer in simplest radical form.

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Answer 1 · 2018-05-30T22:42:11

I got: #2sqrt(3)#

onsider the diagram:
enter image source here

We can use Pythagoras on the violet triangle to get:

#a^2=(a/2)^2+(sqrt(6))^2#

#a^2=a^2/4+6#

#4a^2-a^2=24#

#a^2=24/3#

#a^2=8#

#a=sqrt(8)#

The area of the complete triangle will then be:

#"Area"=("base"xx"height")/2=(sqrt(8)xxsqrt(6))/2=(sqrt(4*2)xxsqrt(6))/2=2/2sqrt(2)sqrt(6)=sqrt(12)=2sqrt(3)#