Question 1205049
<pre>
Area of the segment marked with X:

{{{drawing(200,200,-.7,.7,-.2,1.2,locate(-.08,.3,55^o),locate(-.53,.5,16cm),
line(.46,.88,0,0),line(-.46,.88,0,0),line(.46,.88,-.46,.88),arc(0,0,2,-2,62.5,117.5),locate(-.04,.98,X) )}}}

The area of the whole sector is  

{{{A=expr(1/2)r^2*theta*expr(pi/180^o)=expr(1/2)*(16)^2*(55^o*expr(pi/180))=122.8711793)}}}

The area of the triangle is

{{{A=(a)(b)sin(theta) = 16*16*sin(55^o)=104.8514617}}}

Answer = area of sector - area of triangle = 122.8711793-104.8514617 =

18.0197176 cm<sup>2</sup>

Edwin</pre>