The area of sector bounded by 135 ° arc is 42.42 cm ².
Step-by-step explanation:
Given :-
Radius of the circle , r = 6 cm
Angle of the circle, θ = 135 °
To Find :-
Area of circle bounded by a 135 ° arc.
Solution :-
We know that
[tex]\small \sf \: Area \: of \: sector \: = \frac{θ}{360} \: \times \pi \times r {}^{2} \\ [/tex]
Substitute the values of r and θ , we get
Area of sector =
[tex]\small \sf \: Area \: of \: sector \: = \frac{135 °}{360} \: \times \pi \times {6cm}^{2}\\ [/tex]
[tex]\small \sf \: Area \: of \: sector \: = \frac{135°}{360} \: \times \frac{22}{7} \times 6cm \times 6cm \\ \\ \small \: \sf Area \: of \: circle \: = \frac{135}{360} \times \frac{22}{7} \times 36cm {}^{2} \\ \sf \: \: = \frac{135}{10} \times \frac{22}{7} \\ \sf \: = 42.42cm \: {}^{2} [/tex]
Therefore, The area of sector bounded by 135 ° arc is 42.42 cm ².
