Answer :

ahmedmido1595

[tex]363.9ft^{2}[/tex]

Step-by-step explanation:

[tex]Area =\pi r^{2} -\frac{1}{3}\pi r^{2} +\frac{1}{2}r^{2}sin\alpha \\\\\\ = \frac{2}{3}\pi 12^{2} +\frac{1}{2}12^{2}sin120 =363.9ft^{2}[/tex]

Answer:

363.9 ft²

Step-by-step explanation:

The required area is the area of the circle - shaded area

area of circle = πr² = π × 12² = 144π ft²

shaded area = area of sector - area of Δ NBW

area of sector = πr² × [tex]\frac{120}{360}[/tex] = 144π × [tex]\frac{1}{3}[/tex] = 48π

area of Δ = [tex]\frac{1}{2}[/tex] × 12 × 12 × sin120° = 72 × sin120° ≈ 62.35 ft²

Then

shaded area = 48π - 62.35 ≈ 88.45 ft²

area not shaded = 144π - 88.45 ≈ 363.9 ft²

                   

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