A sector of a circle with radius 21cm has an area of 280cm calculate the perimeter of the sector

Answer 1

To find the perimeter of the sector, we need to find the length of the arc and the two radii of the sector.

The area of the sector is given by the formula:

Area = (θ/360) x π x r^2

280 = (θ/360) x π x 21^2
280 = (θ/360) x 441π
280 = (θ/360) x 1386

θ = (280 x 360) / 1386
θ ≈ 72.77 degrees

Now, we can find the length of the arc using the formula:

Arc Length = (θ/360) x 2 x π x r
Arc Length = (72.77/360) x 2 x π x 21
Arc Length ≈ 36.39cm

The perimeter of the sector is the sum of the arc length and the two radii:

Perimeter = 36.39 + 21 + 21
Perimeter = 78.39cm

So, the perimeter of the sector is 78.39cm.