Answer:
(6+3√3)/2
Step-by-step explanation:
ΔANH is a 30°-60°-90° right triangle. The side lengths of such a triangle are in the ratio 1 : √3 : 2. This means side NH has length √3, and segment NC has length 3. The altitude CH is then 2√3, so the radius of the circle is √3.
The area of triangle CHN is ...
(1/2)(√3)(3) = (3/2)√3
The area of triangle CHM is ...
(1/2)(2√3)(√3) = 3
Then the area of quadrilateral CMHN is ...
3 + (3/2)√3 = (6+3√3)/2
