Question

To the nearest tenth, what is the area of the shaded segment when AG = 6 ft?

Answer 1

A. 10.3 assuming that 113.1 is given

Answer 2

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. $\implies\,\theta=90^{\circ}$

Area of Sector = $\frac{\theta}{360}\times\pi r^2$

Area of Sector AGBA = $\frac{90}{360}\times3.14\times6^2$

                                   = $\frac{1}{4}\times3.14\times36$

                                   = $28.26\:ft^2$

ΔAGB is a right angled triangle.

So, Area of ΔAGB = $\frac{1}{2}\times AG\times GB$

                              = $\frac{1}{2}\times6\times6$

                              = $6\times3$

                              = $18\:ft^2$

Area of Shaded Segment  = 28.26 - 18 = 10.26 ≈ 10.3 ft²

Therefore, Option A  is correct.