Answer:
Step-by-step explanation:
Triangle OCB is equilateral; all sides have length 4 cm. The area of this triangle is A = (1/2)(base)(height) = (1/2)(4 cm)(4 cm)(sin 60°), or
A = (8 cm^2)(√3 / 2), or 4√3 cm^2. The pie-shaped slice OCB has central angle 60°, and the area of the entire circle is π(4 cm)^2. We subtract the area of the triangle from the area of the slice OCB, obtaining:
Smaller red area = A = π(4 cm)^2 - 4√3 cm^2.
The larger red area is found in a similar manner. The central angle AOC is 120°, which is 1/3 of a full circle. Thus, the larger pie-shaped area is
A = (1/3)(π [4 cm]^2] ), and the area of triangle AOC is (1/2)(base)(height), or
(1/2)(4 cm)(4 cm)(sin 60°), or 8/√2 cm^2.
Thus, the larger red area is A = (1/3)(π [4 cm]^2] )(8/√2 cm^2)
