How do I solve for the area and perimeter of the yellow region?

Find the area of the circle: pi*8*8.

Find the ratio of interest=100/360=r=.278

Segment is the radiuses and arc on the end.

The area of the segment is area of the circle times the ratio(.278)

Call the unknown area the eye.

Draw a line thru the eye top to bottom TB

Draw a line center to center thru the circles, lt rt LR.

Find E where they intersect.(center of eye).

RET is a rt triangle with angle of 50 and hyp=8.

8sin(50)= h   8cos(50)=b   area=1/2bh

2 times this= area RTB

subtract the triangle from the segment.

This is the area of 1/2 eye.

Perimeter P = 2*(100/360)*2π*8 = 80π/9 ~ 27.925

The central angle θ is (100/360)*2π = 5π/9

For half of the yellow area, the segment is given by A = (1/2)r^2[θ - sin(θ)]

The total yellow area is 64[5π/9 – sin(5π/9)] ~ 48.673 sq units

This drawing is not well labeled or to scale. But I can guess at what's going on. 

The dot should be the center of each circle. The radius of the circle is 8. You can use that to get the circumference of the circle. Look up the formula for the circumference. The angle between the two radii of each circle is 100 (degrees). A circle has 360 degrees. So the arc length is 100/360 of the circumference.

The perimeter is two of the arcs, one from each circle.

Then look up the formula for the area of a circle. You can figure that out from the radius too. Then look at one circle only, and get the area of the part contained between the 2 radii lines and the arc. It's 100/360 of the area of the circle.  (I wish I had a picture of this for you.)Now drop a line straight down to connect the points where each radius intersects the circle. Find the area of the triangle that you just made. If you take the area of the part contained between the 2 radii lines and the arc, and subtract the area of the triangle, you get the area of half of the yellow. (The line that you drew cuts the yellow part in half. To get the area of the whole yellow part, you need to multiply by 2.