Answer:
Option A is correct.
Step-by-step explanation:
Given:
AG = 6 ft ⇒ Radius of the circle , r = 6 ft
⇒ GB = AG = 6 ft
To find: Area of shaded Segment.
Area of Shaded Segment = Area of Sector AGBA - Area of Δ AGB
Sector AGBA forming 90° angle at center. [tex]\implies\,\theta=90^{\circ}[/tex]
Area of Sector = [tex]\frac{\theta}{360}\times\pi r^2[/tex]
Area of Sector AGBA = [tex]\frac{90}{360}\times3.14\times6^2[/tex]
= [tex]\frac{1}{4}\times3.14\times36[/tex]
= [tex]28.26\:ft^2[/tex]
ΔAGB is a right angled triangle.
So, Area of ΔAGB = [tex]\frac{1}{2}\times AG\times GB[/tex]
= [tex]\frac{1}{2}\times6\times6[/tex]
= [tex]6\times3[/tex]
= [tex]18\:ft^2[/tex]
Area of Shaded Segment = 28.26 - 18 = 10.26 ≈ 10.3 ft²
Therefore, Option A is correct.
