Question

find the area of the shaded sector of the circle.
20 ft
the area of the shaded sector is \\(\square\\) \\(\text{ft}^2\\).
(simplify your answer. type an exact answer in terms of \\(\pi\\).)

Explanation:

Step1: Determine the central angle of the shaded sector

The unshaded sector has a right angle (90°), so the central angle of the shaded sector is \( 360^\circ - 90^\circ = 270^\circ \).

Step2: Recall the formula for the area of a sector

The formula for the area of a sector with radius \( r \) and central angle \( \theta \) (in degrees) is \( A=\frac{\theta}{360^\circ}\times\pi r^{2} \). Here, \( r = 20 \) ft and \( \theta = 270^\circ \).

Step3: Substitute the values into the formula

Substitute \( \theta = 270^\circ \) and \( r = 20 \) into the formula:

$$
LATEXBLOCK0
$$

Answer:

\( 300\pi \)