- The formula for the area of a sector is given as: θ/360 x πr²
where:
θ = central angle
r = radius of the sector
In the question, we are given the following parameters:
Radius of the sector = 4cm
Arc length = 1.396 cm
- Step 1: We are not given the central angle, so we have to find it using the arc length formula.
Arc length = θ/360 x 2πr
Hence,
1.396 = θ/360 x 2 x π x 4
Cross Multiply
1.396 x 360 = θ x π x 8
502.56 = θ x 25.132741229
θ = 502.56/25.132741229
θ = 20°
The central angle is 20°
- Step 2: We find the area of the sector
Formula = θ/360 x πr²
= 20/360 x π x 4²
= 2.7925268032 cm²
Approximately to the nearest thousandth = 2.793 cm²
Therefore. the area of the sector is 2.793 cm²
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