if the shaded area has has an angle the measures 84%, Find the area of the shaded region if JK = 3 ft (1 point) Responses 12.6 ft2 12.6 ft2 9.9 ft2 9.9 ft2 15.7 ft2 15.7 ft2 6.6 ft2
To find the area of the shaded region, we first need to find the radius of the circle. Since JK is the diameter of the circle, we can divide it by 2 to get the radius:
Radius = 3 ft / 2 = 1.5 ft
Next, we can use the formula for the area of a sector of a circle:
Area = (θ/360) * π * r^2
Where θ is the angle in degrees and r is the radius.
Given that the angle is 84% of 360 degrees, we can find the angle in degrees:
Angle = 84% * 360 degrees = 0.84 * 360 degrees = 302.4 degrees
Now we can calculate the area of the shaded region:
Area = (302.4/360) * π * (1.5)^2
Area = 0.84 * 3.14159 * 2.25
Area ≈ 6.67 ft^2
Therefore, the area of the shaded region is approximately 6.6 ft^2. The closest answer choice is 6.6 ft^2.