Question

The measure of central angle XYZ is 1.25π radians. What is the area of the shaded sector?

a) 10π units²
b) 20π units²
c) 30π units²
d) 40π units²

Answer 1

To find the area of the shaded sector, use the formula (theta/2) * r^2 where theta is the measure of the central angle in radians and r is the radius of the circle.

Step-by-step explanation:

To find the area of the shaded sector, we need to use the formula for the area of a sector of a circle, which is given by:

Area = (theta/2) * r^2

where theta is the measure of the central angle in radians and r is the radius of the circle. In this case, the measure of central angle XYZ is 1.25π radians. Let's say the radius of the circle is r units. The area of the shaded sector can be calculated as:

Area = (1.25π/2) * r^2 = (1.25/2) * π * r^2 = 0.625 * π * r^2

Since the options for the answer are given in terms of π, we can simplify by multiplying 0.625 * r^2 and then compare it with the given options to find the correct answer.