A sector of a circle with radius 21cm has an area of 280cm
Calculate the perimeter of the sector
To find the perimeter of the sector, we need to calculate the arc length (the curved part of the boundary of the sector) and add it to the sum of the two radii forming the sector.
First, let's calculate the angle of the sector:
Area of the sector = (θ/360) * π * r^2
280 = (θ/360) * π * 21^2
280 = (θ/360) * π * 441
θ = (280 * 360) / (π * 441)
θ ≈ 93.14 degrees
Now, let's calculate the arc length:
Arc length = (θ/360) * 2 * π * r
Arc length = (93.14/360) * 2 * π * 21
Arc length ≈ 33.51 cm
Finally, let's calculate the perimeter of the sector:
Perimeter = Arc length + 2 * r
Perimeter = 33.51 + 2 * 21
Perimeter = 33.51 + 42
Perimeter = 75.51 cm
Therefore, the perimeter of the sector is approximately 75.51 cm.