Question

How do you solve for the segment area in a circle?

Answer 1

The area of the entire sector of DEF = 60 / 360 * PI * radius^2
sector area = 1 / 6 * 3.14159265... * 20^2
sector area = 209.4395102393

segment area = sector area - triangle DEF Area
triangle DEF Area = (1/2) * 20 * sine 60 * 20
triangle DEF Area = (1/2) * 0.86603 * 400
triangle DEF Area = (1/2) * 346.412
triangle DEF Area = 173.206

segment area = 209.4395102393 -173.206

segment area = 36.2335102393
segment area = 36.23 m

Source:
http://www.1728.org/circsect.htm