karthikpandian19 wrote:In the circle shown in the picture, the radius is 6 and chord AB = 6. What is the area of the shaded region?
(refer the image for other details)
Area of the shaded region = Area of the sector - Area of the triangle OAB
OAB is an equilateral triangle, as all sides are equal. So, each of the angles will be 60 degrees each.
Area of sector = (1/2) * angle subtended at the center of circle * (pi)/180 * r² = (1/2) * 60 * (pi)/180 * 6² = 6(pi)
Length of perpendicular from vertex O to the base AB = √(6)² - (3)² = √27 = 3√3
Area of triangle OAB = (1/2) * 6 * 3√3 = 9√3
Therefore, area of shaded region = 6(pi) - 9√3
The correct answer is
E.
