An equilateral triangle with side of is inscribed in a circle. what is the area of one of the sectors formed by the radii to the vertices of the triangle?

Let ABC the vertices of the EQUILATERAL triangle inscribed in the circle centered in O & with R as radius (sketch it to better understand)
Join OA & OB so that to calculate the area of sector BOA
Mesure Angle C = 1/2 mes Arc AB, but C =60° , then Arc AB = 120°
So the central angle AOB = mes ARC OAB = 120°
The area of a sector = mes angle BOA x R² (mind you angle should be in radian) Angle BOA = 120°or 2π/3 (in radian) the Area Sect = (2π/3).R²

Really long apparently

Photo math will give you the step by step answer : )