What is the area of an equilateral triangle that has a perimeter of 18 centimeters?

1 Answer
Alan P.
Jan 26, 2016

Area #= 9sqrt(3)# sq. cm.

Explanation:

If the perimeter of an equilateral triangle is #18# centimeters
#color(white)("XXX")#each side is #6# centimeters long
and
#color(white)("XXX")# the semi-perimeter, #s#, is #9# centimeters long.

Using Heron's formula With sides #a=b=c=6# and #s=9#
#color(white)("XXX")"Area"_triangle = sqrt(s(s-a)(s-b)(s-c))#

#color(white)("XXXXXXX")=sqrt(9xx3xx3xx3)#

#color(white)("XXXXXXX") = 9sqrt(3)#

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