Question

Express answer in exact form.

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

Answer 1

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

Answer 2

A = { 32/3 π - 16 √ 3 } in^2

Explanation:

Hope this helps.