Area calculation

The yellow region is a segment of a circle. Draw $OC$ and $OD$ to form a sector of a circle. Apply pythagorean theorem in $\triangle CAO$ .

$(CA)^2=17^2-8^2$

$(CA)^2=225$

$CA=\sqrt{225}$

$CA=15$ $\text{feet}$

It follows that,

$CD=2(CA)=2(15)=30$ $\text{feet}$

Apply cosine law in $\triangle CDO$ ,

$30^2=17^2+17^2-2(17)(17)(cos~\angle COD)$

$cos~(\angle COD)=-\frac{161}{289}$

$\angle COD=cos^{-1}(-\frac{161}{289})\approx 123.855^\circ$

Calculate the area of the sector:

$A_{sector}=\frac{\angle COD}{360}(\pi)(r^2)=\frac{123.855}{360}(3.14)(17^2)\approx 312.2~ft^2$

Calculate the area of the triangle:

$A_{T}=\frac{1}{2}(b)(h)=\frac{1}{2}(30)(8)=120`ft^2$

Calculate the area of the segment:

$A=A_{sector}-A_{T}=312.2-120=192.2~ft^2$

Based from the given options, the nearest area of the yellow region is $192~ft^2$ .