9514 1404 393
Answer:
781.4 cm²
Explanation:
The shaded region consists of four (4) 30° sectors and eight (8) 60° segments. The formulas for the areas of these figures can be used.
area of sector = (1/2)r²θ
area of segment = (1/2)r²(θ -sin(θ))
For radius r, the area of the 4 sectors is ...
sector area = 4(1/2)(r²)(π/6) = (π/3)r²
and the area of the 8 segments is ...
segment area = 8(1/2)(r²)(π/3 -sin(π/3)) = 4r²(π/3 -√3/2) = (4/3)πr² -r²(2√3)
So, the total shaded area is ...
shaded area = r²(π/3 +4π/3 -2√3)
The radius of the circle is 21 cm, so the shaded area is ...
(21 cm)²(5π/3 -2√3) ≈ 781.4 cm²