Area of square = length * width or side * side , as 'S' is length of one side
Sum of 4 sides of square = perimeter of square, so
4S = p .... (1)
Hexagon has 6 sides, so perimeter T is 6 * side of hexagon = 6*h
6h = T or
h = [tex]\frac{T}{6}[/tex] .... (2)
We have to find h + p in terms of 's' and 't' so, adding (1) and (2) we get
[tex]\frac{T}{6}+4S[/tex]
The value of h+p in terms of s and t is:
[tex]h+p=\dfrac{t}{6}+4s[/tex]
Perimeter of a polygon--
It is the sum of all the the side lengths of a polygon.
Now, we are given a square whose side length is: s units
and perimeter is: p units
This means that:
[tex]p=s+s+s+s[/tex]
( since, there are 4 sides in a square and all sides are of equal length )
Hence, we get:
[tex]p=4s[/tex]
Also, we are given a regular hexagon ( i.e. the hexagon is equilateral and equiangular) with side length h and perimeter t.
This means that:
[tex]t=h+h+h+h+h+h[/tex]
( since there are 6 sides in a hexagon)
Hence, we have:
[tex]6h=t\\\\i.e.\\\\h=\dfrac{t}{6}[/tex]
Now,
[tex]h+p=\dfrac{t}{6}+4s[/tex]
