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

Answer 1

Claire Akin

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

#"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#

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Answer 2

Avery Allen

To find the area of an equilateral triangle with a given apothem, you can use the formula:

[ \text{Area} = \frac{3}{2} \times \text{apothem}^2 \times \sqrt{3} ]

Where the apothem is the perpendicular distance from the center of the triangle to one of its sides. Simply plug in the given value of the apothem into this formula to find the area of the equilateral triangle.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.