What is the area of a equilateral triangle with a side of 12?

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What is the area of a equilateral triangle with a side of 12?

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Answer 1 · 2014-12-09T02:28:30

The formula for the Area of an equilateral triangle with side s is $A = \frac{s^{2} \sqrt{3}}{4}$ $A= (s^2sqrt(3))/4$

For an equilateral triangle, the sides are equal and the angles are equal. So each angle is 60 degrees. If we are to drop a vertical line from the vertex angle we divide the opposite side in two equal parts. The vertex angle is also equally divided into two. Thus, we form a 30°-60°-90° triangle.

The height , h, of the right triangle in terms of the sides (s) of the equilateral triangle is $\frac{s \sqrt{3}}{2}$ $(ssqrt(3))/2$

This height is also the height of the equilateral triangle whose base is s.

Generally the Area of any triangle is,

$A = \frac{(b a s e) \cdot (h e i g h t)}{2}$ $A =( (base)*(height))/2$

plugging in the values,

$A = \frac{(s) \cdot \frac{s \sqrt{3}}{2}}{2}$ $A = [(s)*(ssqrt(3))/2]/(2)$

$A = \frac{s^{2} \sqrt{3}}{4}$ $A = (s^2sqrt(3))/4$

$s = 12$ $s = 12$

$A = \frac{12^{2} \sqrt{3}}{4}$ $A = (12^2sqrt(3))/(4)$

$A = 36 \sqrt{3}$ $A = 36sqrt(3)$ square units

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What is the area of a equilateral triangle with a side of 12?

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