The semicircle shown at left has center X XX and diameter W Z ‾ WZ start overline, W, Z, end overline. The radius X Y ‾ XY start overline, X, Y, end overline of the semicircle has length 2 22. The chord Y Z ‾ YZ start overline, Y, Z, end overline has length 2 22. What is the area of the shaded sector formed by obtuse angle W X Y WXYW, X, Y?
Accepted Solution
A:
Triangle XYZ is equilateral, so the central angle of the sector is 120°, or 2π/3 radians. The area of a sector of central angle β is given by .. A = (1/2)r^2*β . . . . . . β in radians Your sector's area is .. A = (1/2)*2^2*(2π/3) = 4π/3 . . . . square units