Question

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?

Answer 1

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