Question

The semicircle shown at left has center xxx and diameter \overline{wz} wz start overline, w, z, end overline. The radius \overline{xy} xy start overline, x, y, end overline of the semicircle has length 222. The chord \overline{yz} yz start overline, y, z, end overline has length 222. What is the area of the shaded sector formed by obtuse angle wxywxyw, x, y? Choose 1 answer: \dfrac{2}{3}\pi

Answer 1

Thank you for asking this question. Here is your answer:

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

Your sector's area is

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

If there is any confusion please leave a comment below.