To find the area of a sector, you can use the formula:
\[ \text{Area} = \frac{1}{2} r^2 \theta \]
where \( r \) is the radius and \( \theta \) is the angle in radians.
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Find the radius: The diameter is given as \( 16 , \text{fy} \), so the radius \( r \) is half of the diameter: \[ r = \frac{16 , \text{fy}}{2} = 8 , \text{fy} \]
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Substituting the values: Now, substitute \( r = 8 , \text{fy} \) and \( \theta = \frac{\pi}{2} \) into the area formula: \[ \text{Area} = \frac{1}{2} (8 , \text{fy})^2 \left(\frac{\pi}{2}\right) \]
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Calculate the area: \[ \text{Area} = \frac{1}{2} (64 , \text{fy}^2) \left(\frac{\pi}{2}\right) \] \[ \text{Area} = \frac{64 \pi}{4} , \text{fy}^2 \] \[ \text{Area} = 16 \pi , \text{fy}^2 \]
Therefore, the area of the sector is \( 16 \pi , \text{fy}^2 \).