Answer: So the area of the sector with a central angle of 9.6 radians and a radius of 21.4 units is approximately 1438.47 square units.
Step-by-step explanation: To find the area of a sector, we can use the formula:
A = (θ / 2π) * πr^2
Where θ is the central angle of the sector in radians, π is the constant approximately equal to 3.14, and r is the radius of the sector. In this case, θ is 9.6 radians and r is 21.4 units, so we can plug those values into the formula to get:
A = (9.6 / 2π) * π * 21.4^2
Simplifying, we get:
A = (9.6 / 6.28) * 3.14 * 461.96
This simplifies to:
A = 1.5 * 3.14 * 461.96
And finally, to get the area of the sector we multiply to get:
A = 1.5 * 3.14 * 461.96 = 1438.47 square units
So the area of the sector with a central angle of 9.6 radians and a radius of 21.4 units is approximately 1438.47 square units.