Calculate the area of the figure bounded by the arc CD and the chord CD

Calculate the area of the figure bounded by the arc CD and the chord CD if the degree measure of the arc is 150 ° and the radius of the circle is 12 cm.

The area of the required figure is the area of the part of the circle cut off by the chord CD, that is, the area of the segment.

The area of the segment is equal to the difference between the areas of the sector bounded by the radii OC, OD and the arc CD and the area of the triangle OCD.

Sseg = π ^ 2 * α / 360 = 12 ^ 2 * 150/360 = 60 * π cm2.

Sosd = (CO * OD * Sin150) / 2 = (12 * 12 * (1/2)) / 2 = 36 cm2.

Ssec = Sseg – Sosd = 60 * π – 36 = 12 * (5 * π – 3) cm2.

Answer: The area of the figure is 12 * (5 * π – 3) cm2.