The figure below shows two half circles at the end of a rectangle with the dimensions shown. which is closest to the area of the figure in square inches. 75 95 106 154

What I get from your description is that the rectangle has height 5 and length 15. Also, since the semi circles are at each end of the sides of the rectangle there are two possible pictures (see attached). The semi-circles (what you call half circles) can be attached to the short sides or the long sides.

My attached picture has two diagrams one for each case (attached to long sides or short sides). I labeled them A and B so let's do A (the semi circles are attached to the short sides of the rectangle).

A
The area of a rectangle is given by A = length x width.
The area of the rectangle in the picture is (15)(5)=75 square inches.
The area of a circle is where r is the radius. The length of 5 you see is the diameter (it goes all the way across the circle through the center. The radius is half of this so it is 5/2 = 2.5
The area of the semi circles is the same so if we put them together we would get a whole circle. The area of this circle is square inches.
The area of the whole figure is what we get when we add the area of the circle and rectangle. Since none of the answer choices have pi in them let's use 3.14 as an approximation for pi. The whole figure has area: which makes 95 the right answer.

B
If the semi circles are attached to the long side of the rectangle the total area is given by the following (read section A for HOW it's found): As this is NOT one of the answer choices so my guess is your picture looks like A.