The perimeter of a certain sector of a circle of radius 5.6 m is 20.0 m . Find the area of the sector. 4 marks each.
Explanation
To find the area of the sector, we need to use the formula for the area of a sector of a circle: A = (θ / 360) × πr^2, where θ is the central angle and r is the radius. We are given the perimeter of the sector, which is 20 m. The perimeter of a sector is given by the formula P = 2r + (θ / 360) × 2πr. We can rearrange this formula to solve for θ: θ = (P - 2r) / (2πr / 360). Substituting the given values, we get θ = 60°. Now we can find the area of the sector using the formula: A = (60 / 360) × π(5.6)^2 = 9.8 m^2.
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