To calculate the area shaded green, we first calculate the sum of areas S=A1+A2+A3. The green area is the area of circle A less the sum of white areas S.
Also, note that the
area of an equilateral triangle with side s
=(sqrt(3)*s)*s/2
=sqrt(3)*s^2/2.
Proceeding,
A1
=sqrt(3)s^2/2
=sqrt(3)7^2/2
=49sqrt(3)/2
A2
=60/360 of the area of the circle
=60/360*(pi r^2)
=1/6*(pi*7^2)
=49pi/6
A3=A1
=49sqrt(3)/2
S=A1+A2+A3
=49sqrt(3)/2+49pi/6+49sqrt(3)/2
=49sqrt(3)+49pi/6
=49(sqrt(3)+pi/6)
Area shaded green
= pi r^2 - S
=pi 7^2 - S
=49pi - 49(sqrt(3)+pi/6)
=49(5pi/6-sqrt(3))
