Calculate the area of the shaded figure if BО = 3 cm, angle AOB = 120 degrees.

To find the area of a shaded figure, we will use the rule below:

The area of a segment of a circle is equal to the difference between the areas of a circular sector and a triangle formed by two radii and a chord that contracts the arc of the segment.

1) Find the area of the circular sector:

BO = 3 (radius), angle AOB = 120 °. Ssect = πR² * α / 360 = π3² * 120/360 = n9 / 3 = 3π.

2) Find the area of the triangle we need:

Saob = (1/2) * R²Sin120 (Sin120 = Sin (180 – 60) = Sin60 = √3 / 2);

Saob = (1/2) * 9 * √3 / 2 = 9 * √3 / 4.

3) Find the area of the shaded figure (segment area):

Ssect – Saob = 3π – 9 * √3 / 4.

Answer: 3π – 9 * √3 / 4