Question

What is the total area of the shaded triangles?

Answer 1

Check the picture below.

$\bf \textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4}~~ \begin{cases} s=length~of\\ \qquad a~side\\ ------\\ s=\frac{s}{3} \end{cases}\implies A=\cfrac{\left( \frac{s}{3} \right)^2\sqrt{3}}{4} \\\\\\ A=\cfrac{\frac{s^2\sqrt{3}}{3^2}}{4}\implies A=\cfrac{s^2\sqrt{3}}{4\cdot 3^2}\implies A=\cfrac{s^2\sqrt{3}}{36} \\\\\\ \textit{and since there are 3 triangles shaded with that area} \\\\\\ \textit{shaded area}\implies 3\left( \cfrac{s^2\sqrt{3}}{36} \right)\implies \cfrac{s^2\sqrt{3}}{12}$