Answer:
Perimeter of the figure is 2r([tex]\pi[/tex] + 6)
Step-by-step explanation:
Perimeter of a shape is total length of the boundaries of the shape. In the given question, we have two semicircles and a rectangle.
The circumference of a circle = 2[tex]\pi[/tex]r, thus the length of the arc of a semicircle = [tex]\pi[/tex]r.
The height of the rectangle is h, radius 'r' of the semicircle = [tex]\frac{h}{2}[/tex]
⇒               h = 2r
The perimeter of a rectangle = 2(l +b).
Given that: the length is twice its height, so that:
length = 2h
Perimeter of the rectangle = 2 (2h + h)
                      = 6h
But, Â Â Â Â h = 2r
Perimeter of the rectangle = 6 × 2r Â
                      = 12r   Â
Perimeter of the figure in terms of the semicircle's radius = [tex]\pi[/tex]r + 12r  + [tex]\pi[/tex]r
                                                = 2[tex]\pi[/tex]r + 12r
                                          = 2r([tex]\pi[/tex] + 6)
