6.41 m² ( 2 dec. places)
area of sector(A) = area of circle × fraction of circle
A = πr² × [tex]\frac{15}{360}[/tex]
= π × 7² × [tex]\frac{15}{360}[/tex]
= (49π × 15)/360 = 6.41
The area of the sector to two decimal places is 6.41m
The formula for calculating the area of a sector is expressed as:
[tex]A_s=\frac{\theta}{360} \times \pi r^2\\[/tex] where:
r is the radius of the sector
[tex]\theta[/tex] is the angle subtended by the sector
Given the following:
θ = 15°
r = 7 m
Substitute the given parameters into the formula
[tex]A_s=\frac{15}{360} \times \pi (7)^2\\A_s=\frac{15}{360} \times 49\pi \\A_s = \frac{15}{360} \times 153.86\\A_s=\frac{2307.9}{360}\\A_s=6.41m[/tex]
Hence the area of the sector to two decimal places is 6.41m.
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