The area of the sector is 472.6 ft²
<h3>Area of a Sector</h3>
For finding the area of the sector, you need apply the formula:
, where:
r= radius
α= central angle
The question gives:
r= radius= 19 ft
α= central angle = 150°
Thus, the area of the sector will be:

Read more about the area of a sector here:
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Answer:




Step-by-step explanation:
The diagonals of a rhombus are perpendicular to each other, so angles (2) and (3) are equal 90°.
To find angle (1), we can use the sum of internal angles in the left triangle with angles 52°, (1), and (2):



The diagonals of a rhombus bisects the angles, to the angle next to the angle of 52° is also 52°, then, in the upper triangle, we have:


notice, the circle is missing 1/4, so the area of it is just 3/4 of the whole area of the circle.
![\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=8 \end{cases}\implies A=\pi 8^2\implies A=64\pi \\\\\\ \stackrel{whole}{\cfrac{4}{4}}-\stackrel{one~quarter}{\cfrac{1}{4}}=\cfrac{3}{4}~\hfill \cfrac{3}{4}\cdot 64\pi \implies 48\pi \implies \stackrel{\pi =3.14}{150.72} \\\\\\ ~\hspace{34em}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20circle%7D%5C%5C%5C%5C%20A%3D%5Cpi%20r%5E2~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D8%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Cpi%208%5E2%5Cimplies%20A%3D64%5Cpi%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7Bwhole%7D%7B%5Ccfrac%7B4%7D%7B4%7D%7D-%5Cstackrel%7Bone~quarter%7D%7B%5Ccfrac%7B1%7D%7B4%7D%7D%3D%5Ccfrac%7B3%7D%7B4%7D~%5Chfill%20%5Ccfrac%7B3%7D%7B4%7D%5Ccdot%2064%5Cpi%20%5Cimplies%2048%5Cpi%20%5Cimplies%20%5Cstackrel%7B%5Cpi%20%3D3.14%7D%7B150.72%7D%20%5C%5C%5C%5C%5C%5C%20~%5Chspace%7B34em%7D)