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√(3)}{4}~~ \begin{cases} s=length~of\\ \qquad a~side\\ ------\\ s=(s)/(3) \end{cases}\implies A=\cfrac{\left( (s)/(3) \right)^2√(3)}{4} \\\\\\ A=\cfrac{(s^2√(3))/(3^2)}{4}\implies A=\cfrac{s^2√(3)}{4\cdot 3^2}\implies A=\cfrac{s^2√(3)}{36} \\\\\\ \textit{and since there are 3 triangles shaded with that area} \\\\\\ \textit{shaded area}\implies 3\left( \cfrac{s^2√(3)}{36} \right)\implies \cfrac{s^2√(3)}{12}`