Question

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

• A. $\frac{2}{27}{cm}^2$
• B. $\frac{2}{15}{cm}^2$
• C. $\frac{3\sqrt{3}}{64}{cm}^2$
• D. $\frac{3}{14}{cm}^2$

Answer 1

The correct option is C

$\frac{3\sqrt{3}}{64}{cm}^2$

Finding the area of equilateral triangle:

Length of the side of an equilateral triangle $\left(a\right)=$ $\frac{\sqrt{3}}{4}cm$

Area of an equilateral triangle$=\frac{\sqrt{3}}{4}\times a^2$

$$\begin{gathered} =\left(\frac{\sqrt{3}}{4}\times {\left(\frac{\sqrt{3}}{4}\right)}^2\right){cm}^2 \\ =\left(\frac{\sqrt{3}}{4}\times \frac{3}{16}\right){cm}^2 \\ =\frac{3\sqrt{3}}{64}{cm}^2 \end{gathered}$$

Therefore the area of an equilateral triangle has a side length equal to $\frac{\sqrt{3}}{4}cm$ is $\frac{3\sqrt{3}}{64}{cm}^2$

Hence, option (C) is the answer.