Question 45
Consider the tessellated plane with equilateral triangles, and let $F_{0}$ be any of them. A sequence of increasingly larger figures is constructed in this way: $F_{1}$ is the polygon that is obtained by adding to $F_{0}$ the frame formed by all the triangles of the tessellation that touch $F_{0}$ (for a side or by a vertex), $F_{2}$ is the polygon that is obtained by adding to $F_{1}$ the frame formed by the triangles that they touch $F_{1}$, and the following ones are built similarly up to $F_{10}$. How many triangles of the tessellation is this last polygon made up of?
(A) 541
(B) 661
(C) 691
(D) 721
(E) 841 .
(A) 541
(B) 661
(C) 691
(D) 721
(E) 841 .