+4609 A chord of length 6 units divides a circle into two distinct areas. If the circle has a radius of 6 units, what is the area of the larger region, in square units? Express your answer in simplest radical form in terms of \(\pi\) .
+128473
The smaller area between the chord and the edge of the circle is given by :
(1/2)*6^2 (pi/3)- (1/2)*6^2 sin (60) = 36 ( pi/3 - √3/2) (1)
The area of the whole circle = pi (6^2) = 36pi (2)
So the area of the larger part = (2) - (1) =
36pi - 36 ( pi/3 - √3/2) =
36 [ pi - pi/3 + √3/2 ] =
36 [ 2pi / 3 + √3/2] =
[ 24pi + 18√3 ] units^2
