Answer:
The area of the sector (shaded section) is 29.51 [tex]m^{2}[/tex].
Step-by-step explanation:
Area of a sector = (θ ÷ 360) [tex]\pi[/tex][tex]r^{2}[/tex]
where θ is the central angle of the sector, and r is the radius of the circle.
From the diagram give, diameter of the circle is 26 m. So that;
r = [tex]\frac{diameter}{2}[/tex]
= [tex]\frac{26}{2}[/tex] = 13 m
θ = 360 - (180 + 160)
= 360 - 340
= [tex]20^{o}[/tex]
Thus,
area of the given sector = [tex]\frac{20}{360}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](13)^{2}[/tex]
= [tex]\frac{20}{360}[/tex] x x [tex]\frac{22}{7}[/tex] x 169
= 29.5079
The area of the sector (shaded section) is 29.51 [tex]m^{2}[/tex].
