Question

going to work through this geometry problem b/c this is going to bother me all day

Answer 1

area of sector = (60/360)* pi * 2^2

area of the triangle = [sqrt(3)/4] * 2^2

area of the small segment = (60/360)* pi * 2^2 - [sqrt(3)/4] * 2^2 = 2pi/3 - sqrt(3)

Answer 2

area of that circled region = area of the quarter-circle - area of the triangle - area of the small segment

(1/4)pi(2^2) - (60/360)*pi*(2^2) - [2pi/3 - sqrt(3)] = sqrt(3) - pi/3

Answer 3

area of the middle region = area of the whole square - 4(area of that circled region)

= 4 - 4(sqrt(3) - pi/3)