Express answer in exact form.

Given a circle with an 8" radius, find the area of the smaller segment whose chord is 8" long

I'm guessing that you want to find the segment area of a circle that has a radius AO = 8" and a chord AB with a length of 8".

Sine angle AOD = AE / OA

Sine angle AOD = 4 / 8

Sine angle AOD =.5

arc sine (.5) = 30 degrees

So, angle AOB = 60 degrees

Circle Area = PI * radius^2

Circle Area = 201.06

Sector Area = (60/360) * 201.06

Sector Area = 33.51

Line OE^2 = AO^2 - AE^2

Line OE^2 = 64 - 16

Line OE = 6.9282032303

Triangle AOB Area = OE*AE = 6.9282032303 * 4

Triangle AOB Area = 27.7128129211

Segment Area = Sector Area - Triangle AOB Area

Segment Area = 33.51 - 27.71

Segment Area = 5.80