Area of an equilateral triangle as function of triangle’s side length x will be?

1/4x

√3/4x^2

√3/4x

None of these

The height hh of the equilateral triangle is 32x23x.Using the area formula for a triangle (Area=12×base×heightArea=21×base×height):A=12×x×32x=34x2A=21×x×23x=43x2

Explanation

- The height $h$ of the equilateral triangle is $\frac{\sqrt{3}}{2} x$ .
- Using the area formula for a triangle ( $Area = \frac{1}{2} \times base \times height$ ):
  $A = \frac{1}{2} \times x \times \frac{\sqrt{3}}{2} x = \frac{\sqrt{3}}{4} x^{2}$