The area of the sector is equal to half of the square of the radius times the opening of the sector (theta). Basing on the figure, the angle of sector COD is 90 degrees. So,
Area of sector = 50.24 = (1/2) * (r^2) (theta)
The theta should be expressed in radians. So, we convert 90 degrees to radians:
90 degrees (pi rad/180 degrees) = pi/2
Thus,
50.42 = (1/2) * (r^2) * (pi/2)
r^2 = 64.2
r = 8.01 units
Thus, the radius of the sector is 8.1 units.
