CPM Homework Help : GC Problem 8-37

A triangle where from each vertex, a dotted line is drawn to the midpoint of the opposite side. The bottom left right triangle is shaded. Esteban used a hinged mirror to create an equilateral triangle, as shown in the diagram at right. If the area of the shaded region is $11.42$ square inches, what is the area of the entire equilateral triangle? Justify your solution.

Hint:

Each of the triangles is a reflection of another triangle, so all of the triangles are congruent.