The perimeter of an equilateral triangle is 24. What is the area?

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Answer 1 · 2016-04-27T16:48:06

The area # = color(green)(16sqrt3 cm^2 #

The perimeter of an equilateral triangle #(3a)# is #=24 cm# (assuming units to be in cm)

Let us denote the side of the equilateral triangle as #a#

#3a = 24#

#a = 24/3#

#color(green)(a = 8cm#

The formula for area of equilateral triangle is :
#color(blue)(sqrt3/4 (a^2)#

# = sqrt3/4 (8^2)#

# = sqrt3/4 * 64#

# = color(green)(16sqrt3 cm^2 #