Calculate the area of a figure bounded by an arc AB and a chord AB if the degree

Calculate the area of a figure bounded by an arc AB and a chord AB if the degree measure of the arc = 30 deg. and the radius of the circle = 6cm.

Let’s denote the area of the OAB sector through S1, and the area of the triangle ABC through S2, then the required area S is the difference S1 – S2.

Determine the area of the sector:

S1 = π * R ^ 2 * α / 360 = π * 6 ^ 2 * 30/360 = 3 * π cm2.

Determine the area of the triangle AOB:

S2 = (ОА * ОВ * Sin30) / 2 = (6 * 6 * 1/2) / 2 = 9 cm2.

Then S = S1 – S2 = 3 * π – 9 = 3 * (π – 3) cm2.

Answer: The area is 3 * (π – 3) cm2.