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Moderate

Perimeter of Coordinate Figure

ACTMAT-JVIN1E

The figure below consists of a rectangle and two semicircles, one on each end, in the x-y coordinate plane.

If $(4,0)$ and $(18,0)$ are coordinates of two points in the figure where the vertices of the rectangle intersect the endpoints of the diameter of the semicircles, what is the perimeter of the figure?

A

$ 28 + 4\pi $

B

$ 28 + 8\pi $

C

$ 28 + 16\pi $

D

$ 36 + 4\pi $

E

$ 36 + 8\pi $