Question

1. to the nearest tenth, what is the area of the shaded segment when ag = 6 ft? 21.1 ft² 1.7 ft² 10.3 ft² 28.3 ft²

Explanation:

Step1: Calculate the area of the sector

Since \(AG = BG=6\) (radii of the circle) and \(\angle AGB = 90^{\circ}\) (right - angle), the formula for the area of a sector is \(A_{sector}=\frac{\theta}{360}\times\pi r^{2}\), where \(\theta = 90^{\circ}\) and \(r = 6\).

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Step2: Calculate the area of the triangle

The formula for the area of a right - triangle is \(A_{triangle}=\frac{1}{2}\times base\times height\). Here, base \(AG = 6\) and height \(BG = 6\).

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Step3: Calculate the area of the segment

The area of the segment \(A = A_{sector}-A_{triangle}\)

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Answer:

\(10.3\mathrm{ft}^{2}\)