Question 763264
 Express answer in exact form.
Find the area of the larger segment whose chord is 8" long in a circle with an 8" radius.
:
We know that the triangle formed by the two radii and the chord is 
an equilateral triangle, all angles are 60 degrees, which is 1/6 of 
360 degrees
:
Find area inside the 60 degree arc
{{{1/6}}}*{{{pi*8^2}}} =  35.51
:
Find the area of the equilateral triangle
{{{1/2}}}*8*{{{sqrt(8^2-4^2)}}} = 27.71 sq/in
:
Find the area of the shape enclosed by the 60 degree arc and the chord
35.51 - 27.71 = 7.8 sq/in
:
Find the area of the larger segment
{{{pi*8^2}}} - 7.8 = 193.26 sq/inches