Three of these methods gives the correct area of the figure. which method does not?
a. add the areas of two half circles and a trapezoid b. add the areas of a circle, a rectangle and two triangles c. add the areas of a circle and a rectangle. then subtract the area of a trapezoid d. add the areas of two half circles and a rectangle. then subtract the area of a trapezoid

Ah hah !  NOW I see it.  Thanks to BellBell for a good link.

My first impression is a dog bone standing up on one end.

You're talking about the area of the figure, so I'll think that over
before I look at the choices.

I see:

-- 2 semi-circles = 1 whole circle.
and
-- (1 rectangle) minus (a trapezoid).

Now I'll look through the choices.

A).  No good.  The trapezoid is cut OUT of the figure,
and shouldn't be added into it.

B).  Oh ! Yes !  I didn't look at it that way at first, but
I can see how that works.  'B' is good.

C). and D).  Yes.  This was my description above.

So 'A' is the method that's wrong.