Final answer:
The area of sector OAB, with a radius of 23 cm and an angle of 96 degrees, is 521.5 cm², after converting the angle to radians and applying the formula for a sector's area.
Step-by-step explanation:
To calculate the area of sector OAB, we will use the formula for the area of a sector which is \((1/2) \times (\text{radius})^2 \times (\text{angle in radians})\). The angle given is 96 degrees, which needs to be converted into radians to use in the formula. To convert degrees to radians, we multiply by \(\pi/180\). The radius is the length of BA, which is 23 cm.
First, we convert the angle: \(96\degree \times (\pi/180) = 1.68 \text{ radians}\). Now, we can substitute the values into the sector area formula: \((1/2) \times 23^2 \times 1.68 = 521.5 \text{cm}^2\), which is option A.