Question

Express answer in exact form.

A segment of a circle has a 120 arc and a chord of 8sqrt3 in. Find the area of the segment.


HELP ME PLEASE!!!!!

Answer 1

area of sector = 1/3 * pi* r^2
area segment = area sector - area triangle

Answer 2

area of triangle = h * 4sqrt3
h = 4sqrt3 / tan 60
so area of triangle = (4sqrt3)^2/tan60 = 48/tan 60
and r = 4sqrt3/sin60 and area of sector = (1/3) * pi *(4sqrt3/sin60)^2
so now you have all the values necessary to work out the area of the segment

Answer 3

Geometry is not my strong suite so please take my answer with a grain of salt. So I get your radius will be 8/sqrt(3) which makes your area of the circle 64/3(pi). Since the area of sector is (64pi)/9 you will subtract 16sqrt(3)/3 from that... so 64pi/9-16sqrt(3)3