The shaded area is a segment. The area of a segment is
[tex] A_{segment}=A_{sector}-A_{triangle} [/tex].
You know radius that is the side of isosceles triangle and measure of angle between two equal triangle sides, then
[tex] A_{triangle} =\dfrac{1}{2} a\cdot a \sin \alpha=\dfrac{1}{2} 18.6\cdot 18.6 \cdot \sin 123^{\circ}=172.98\cdot \sin 123^{\circ}=145.07 [/tex] sq. m..
The area of sector is [tex] A_{sector}=\dfrac{r^2\cdot \alpha}{2}= \dfrac{(18.6)^2\cdot 0.68\pi}{2}=117.63\pi=369.53[/tex] sq. m..
Then [tex] A_{segment}=369.53-145.07=224.46 [/tex] sq. m.
Answer: [tex] A_{segment}=224.46 [/tex] sq. m.
