Question

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

Answer 1

A. 10.3 assuming that 113.1 is given

Answer 2

Option A is correct.

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 =
`(\theta)/(360)*\pi r^2`

Area of Sector AGBA =
`(90)/(360)*3.14*6^2`

=
`(1)/(4)*3.14*36`

=
`28.26\:ft^2`

ΔAGB is a right angled triangle.

So, Area of ΔAGB =
`(1)/(2)* AG* GB`

=
`(1)/(2)*6*6`

=
`6*3`

=
`18\:ft^2`

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

Therefore, Option A is correct.