Look at the two circles below. They share a center point. The larger circlehas a radius of 10 inches. The distance between the smaller circle and the larger circle is 2 inches. Which best represents the shaded area between the two circles? A138 square inches
138 square inches

B36 square inches
36 square inches

C515 square inches
515 square inches

D314 square inches
314 square inches

trapezoid

step-by-step explanation:

first i plotted all my points on a grid graph

i made sure all of them were in the correct quadrant

then i saw it was a trapezoid or a quadrilateral

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4