How do you find the area of an equilateral triangle with a given apothem?

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Answer 1 · 2018-07-15T02:44:52

#color(blue)("Area of triangle in terms of apothem " A_t = 3 sqrt 3 a^2#

![https://www.slideshare.net/rickamtower/unit-6-area-of-regular-polygons-8598610]( useruploads.socratic.org )

#"Apothem " a = s / (2 * sqrt3)#

where s is the length of the side of an equilateral triangle.

#:. s = 2 sqrt3 a#

#"Area of equilateral triangle " A_t = (sqrt3 s^2 ) / 4#

Substituting for s in terms of a,

#A_t = (sqrt3 / 4) * (2 sqrt3 a)^2#

#A_t = (sqrt3 * cancel4 * 3 * a^2) / cancel4 #

#color(blue)(A_t = 3 sqrt3 a^2#