Question

The radius of the circle is ✓2. The distance from the center to the chord is 1. If the measure of AB is 90°, the area of the shaded region is

Answer 1

c. (π/2 -1) square units

Explanation:

A segment that subtends an arc of θ in a circle of radius r has an area given by ...

A = (1/2)(θ -sin(θ))r² . . . . . where θ is in radians

In your figure, the radius is r = √2 and the angle is 90°, so θ = π/2. Then the area is ...

A = (1/2)(π/2 -sin(π/2))·(√2 units)²

A = (π/2 -1) units²