The area of the figure, bounded by the arc AB and the chord AB, if the degree measure of the arc

The area of the figure, bounded by the arc AB and the chord AB, if the degree measure of the arc AB = 150 degrees, and the radius of the circle = 12 centimeters.

The area of the shaded figure that needs to be determined is the area of the part of the circle cut off by the chord AB, 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 ОА, ОВ and the arc AB and the area of the triangle ОАВ.

Sseg = π ^ 2 * α / 360 = 122 * 150/360 = 60 * π cm2.

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

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

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