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

$Area of triangle in terms of apothem A_{t} = 3 \sqrt{3} a^{2}$ $color(blue)("Area of triangle in terms of apothem " A_t = 3 sqrt 3 a^2$

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$Apothem a = \frac{s}{2 \cdot \sqrt{3}}$ $"Apothem " a = s / (2 * sqrt3)$

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,

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

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

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