Question

Can someone tell me how to solve this please? Can you show the steps!!!

Answer 1

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 = $\pi r+ 2r$

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 = $\pi r+ 2r-2r$  

                                             $=\pi r$                                          

                                             $=\pi \times 2$

                                             = 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.