Y by
Let's construct a family
of geometric figures following the pattern shown in pictures:
where each hexagon (like the starting one) is constructed by cutting the two corners tops of a square, in such a way that the two figures removed are identical isosceles triangles, and the three resulting upper sides have the same length.
Continuing like this, a pattern is produced with which we can build the figures
, for integer
. Then, we denote by
and
the perimeter and area of the figure
, respectively. If the side of square to build
measures
:
(a) Calculate
and
(in terms of the length
).
(b) Find an explicit formula for
, and for
, in terms of
and of
. Simplify your answers.
(c) If
, find the measure of the six sides of the figure
, in its simplest form.


Continuing like this, a pattern is produced with which we can build the figures







(a) Calculate



(b) Find an explicit formula for




(c) If


This post has been edited 1 time. Last edited by parmenides51, Mar 24, 2024, 2:10 PM