What is the area of the shaded region?​ (1) The ratio of length of ar

Q. What is the area of the shaded region ?​

Analyzing the question stem​
Area of shaded region = area of the sector – area of the triangle​
We know to calculate area of the sector, central angle and radius are required.

Analysing the statement
1) The ratio of length of arc ABC to circumference of the circle is 1:6​
Ratio of length of arc to cicumference of the circle = ratio of cental angle to complete angle = 1:6.
Central angle = 1/6 * 360 = 60

Deriving further​
AO = CO = radius and angle AOC = 60. Therefore triangle AOC is equilateral.​

As radius is unknown, area of the shaded region cannot be calculated.
Insufficient​

​2) The area of triangle AOC is 9√3​
Area of the sector is unknown.
Insufficient​

​Combining statement (1) and (2)
area of equilateral traingle = \(\frac{√3}{4}\) \(a^2\) = 9√3​
From this, radius will be calculated and hence sector area.
Sufficient​

C is correct​