Mathematics: To the nearest tenth, what is the area of the shaded segment when ag = 6 ft? 10.3 ft2 21.1 ft2 1.7 ft2 28.3 ft2

second 1Step-by-step explanation:...

To the nearest tenth, what is the area of the

lberries08

13.03.2022

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.

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