Answer:
To find the area of the shaded region, we need to find the area of the sector formed by the shaded angle and subtract the area of the triangle formed by the radius and the two radii at the endpoints of the shaded angle.
The area of the sector can be found using the formula:
Area of sector = (θ/360) x πr²
where θ is the central angle in degrees and r is the radius of the circle.
Here, θ = 130 degrees and r = 21 cm.
Area of sector = (130/360) x π x 21²
= 2471.39 cm²
Next, we need to find the area of the triangle. We can find the height of the triangle using trigonometry.
sin(130 degrees/2) = h/21
h = 21 x sin(65 degrees)
h ≈ 18.12 cm
The base of the triangle is the length of the arc that forms the shaded angle. We can find this length using the formula:
Length of arc = (θ/360) x 2πr
Length of arc = (130/360) x 2π x 21
= 38.81 cm
The area of the triangle is:
Area of triangle = 0.5 x base x height
= 0.5 x 38.81 x 18.12
= 351.70 cm²
Finally, we can find the area of the shaded region by subtracting the area of the triangle from the area of the sector:
Area of shaded region = Area of sector - Area of triangle
= 2471.39 - 351.70
= 2119.69 cm²
Therefore, the area of the shaded region is approximately 2119.69 cm².