A thin plastic band 50 cm long is used to tie seven plastic pipes together. What is the radius of the pipe?

The shape is a hexagon but not vertices but curved.

My solution was , you get an eqilateral triangle with side 3 r
3 r = 50/6
r = 50/6/3
= 2.73

But the text book answer is 25/(pi+6)

4 answers

25 / ( pi + 6 ) =

25 / ( 3.1415926535 + 6 ) =

25 / 9.1415926535 =

2.734753226

approx. = 2.73

What is problem?
How do you get it in terms of pi?
I see pi in Bosnian's calculations.
Where do you get the equilateral triangle with sides 3r from?