An equilateral triangle has a height of #sqrt(6)# units. What is the area of the triangle?

1 Answer
Alan P.
Jan 1, 2018

Area: #=2sqrt(3)# sq. units

Explanation:

A common form for the equilateral triangle looks like:
enter image source here
If this common form is scaled up so that the height is #sqrt(6)#
then since #sqrt(6)=sqrt(3)xxsqrt(2)#
the scaled up base will have a length of #2 xx sqrt(2)# (or just #2sqrt(2)#
(and the height is the given value of #sqrt(6)#

The area of this (scaled up) triangle will be:
#"Area"=1/2 * "base" * "height"#

#color(white)("XXX")=1/2 * 2sqrt(2) * sqrt(6)#

#color(white)("XXX")=sqrt(12)#

#color(white)("XXX")=2sqrt(3)#

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