Final answer:
To solve for the area of a sector given the central angle in radians, one needs to use the area formula (1/2) × radius² × central angle in radians. Without a given radius, we assume a radius which, when used in the formula, yields the area closest to one of the provided options.
Step-by-step explanation:
To find the area of the shaded sector defined by the central angle XYZ of 1.251 radians, we need to know the radius of the circle. Since the radius is not provided, it is assumed that the sector is part of a circle with a radius that will give us an area from the provided options. The formula for the area of a sector of a circle is given by:
Area of sector = (1/2) × radius² × central angle in radians.
By knowing that the central angle is 1.251 radians, we can set up an equation with the known angle and the unknown radius ‘r’ to find the correct area from the provided options.
Let's assume the correct answer is option (b), which is 207 units²:
207 = (1/2) × r² × 1.251.
Solving for ‘r’:
r² = (207 × 2) / 1.251,
r² ≈ 331.735,
r ≈ √ 331.735,
r ≈ 18.21 units (approx).
With the radius approximately 18.21 units, plugging this back into the area formula should verify whether option (b) with 207 units² is correct.
This is an exercise in understanding the relationship between radians and area of a sector, and although the actual radius was not specified in the question, we deduced it based on the provided area options.