Question

What is the area of the shaded region in the given circle in terms of pi and in simplest form?

A. (30 pi + 9 √3) m²
B. (24 pi + 9 √3) m²
C. (30 pi + 18 √3) m²
D. (24 pi + 18 √3) m²

Answer 1

The area of the circular region is:
A1 = ((300/360) * (pi * 6 ^ 2))
Rewriting:
A1 = 30pi
Then, the trig area is:
A2 = (1/2) * (6) * (sine (60) * 6)
A2 = (1/2) * (6) * ((root (3) / 2) * 6)
Rewriting:
A2 = (3) * ((root (3)) * 3)
A2 = (9) * (root (3))
The area of the shaded region is the sum of the areas:
A = A1 + A2
Substituting values:
A = 30pi + 9raiz (3)
Answer:
A. (30 pi + 9 √3) m²