Option B:
The perimeter of the figure is 16 + 2π.
Solution:
The clear image of the question is attached below.
Diameter of the semicircle = 7 – 3 = 4
Radius of the semicircle = 4 ÷ 2 = 2
Perimeter of the semicircle = [tex]\pi r+ 2r[/tex]
In figure, one side of the semicircle is merged with rectangle, so remove two radius from the perimeter of the semicircle.
Perimeter of the semicircle = [tex]\pi r+ 2r-2r[/tex]
[tex]=\pi r[/tex]
[tex]=\pi \times 2[/tex]
= 2π units
Perimeter of the rectangle given = 3 + 7 + 3 + 3
= 16 units
Perimeter of the given figure = 2π + 16
= (16 + 2π) units
Hence the perimeter of the figure is 16 + 2π.
Option B is the correct answer.
