Question

The area of an equilateral triangle having a side length equal to $\frac{\sqrt{3}}{4}$cm is

Answer 1

Given side length is $\frac{\sqrt{3}}{4}\mathrm{cm}$.

Use $A=\frac{\sqrt{3}}{4}{a}^2$ to calculate the area of a triangle:

$\begin{array}{rcl}A& =& \frac{\sqrt{3}}{4}{\left(\frac{\sqrt{3}}{4}\right)}^2\\ & \Rightarrow & A=\frac{\sqrt{3}}{4}\left(\frac{3}{16}\right)\\ & \Rightarrow & A=\frac{3\sqrt{3}}{64}{\mathrm{cm}}^2\end{array}$

Therefore, the area of the equilateral triangle is $\begin{array}{l}\frac{3\sqrt{3}}{64}{\mathrm{cm}}^2\end{array}$.