Question

The semicircle shown at left has center X and diameter WZ. The radius XY of the semicircle has length 2. The chord YZ has length 2. What is the area of the shaded sector formed by obtuse angle WXY

Answer 1

4π/3 square units

Explanation:

Triangle XYZ is equilateral,

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

.. A = (1/2)*2^2*(2π/3) = 4π/3 square units