Hello, Vicky!

On each side of a unit square, an equilateral triangle of side length 1 is constructed.

On each new side of each equilateral triangle, another equilateral triangle of side length 1 is contructed.

The interiors of the square and the 12 triangles have no points in common.

Let R be the region formed by the union of the square and all the trianlges,

and let S be the smallest convex polygon that contains R.

What is the area of the region that is inside S but outside R? Code:

B
*-------*-------o
*:::::*:*:::::* \
* *:::*:::*:::* o C
|::* *:*:::::*:* *::|
|:::::*-------o:::::|
|::*::| A|::*::|
*:::::| |:::::*
|::*::| |::*::|
|:::::*-------*:::::|
|::* *:*:::::*:* *::|
* *:::*:::*:::* *
*:::::*:*:::::*
*-------*-------*

The region is comprised of a unit square and 12 equilateral triangles.

The area of is: .

has two sides and included angle

Its area is: .

The area of is the area of plus four of those triangles.

. .

The area inside and outside is: .