Answer:
[tex]16\pi \text{ yd}^2[/tex]
Step-by-step explanation:
Since, the area of a sector of a circle,
[tex]A=\frac{\theta}{360}\times \pi (r)^2[/tex]
Where, r is the radius of the circle,
[tex]\theta[/tex] ( in degree ) is the central angle formed by the arc of the sector,
By the given diagram,
The radius of the circle, r = AE = 8 yd,
Central angle by the arc AB, [tex]\theta[/tex] = 90°,
Hence, the area of the sector AEB,
[tex]A=\frac{90}{360}\times \pi(8)^2[/tex]
[tex]=\frac{1}{4}\times 64\pi[/tex]
[tex]=16\pi\text{ yd}^2[/tex]
