The area of an equilateral triangle is equal | vedclass

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Question

(D) The area of an equilateral triangle with side length $a$ is given by the formula: Area $= \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$. Fo

Vedclass · Accepted Answer

$\frac{\sqrt{3}}{4}(	ext{side})^2$

Vedclass · Answer

(D) The area of an equilateral triangle with side length $a$ is given by the formula: Area $= \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$. For an equilateral triangle,the base is $a$ and the height $h$ is calculated using the Pythagorean theorem: $h = \sqrt{a^2 - (a/2)^2} = \sqrt{3a^2/4} = \frac{\sqrt{3}}{2}a$. Substituting these values: Area $= \frac{1}{2} 	imes a 	imes \frac{\sqrt{3}}{2}a = \frac{\sqrt{3}}{4}a^2$. Therefore,the correct option is $D$.

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