Respuesta :
The shaded portion is a minor sector with diameter = 28m
therefore,
Radius ,r = diameter/2
Radius, r=28m/2=14m
Next, we have to calculate the angle of the sector
The angle of the sector is connected to the 140° on a straight line
Let the angle of the sector be
[tex]\phi[/tex]Therefore,
[tex]\begin{gathered} \phi+140^0=180^0 \\ \phi=180^0-140^0 \\ \phi=40^0 \end{gathered}[/tex]Then we can calculate the area of a sector using the formula
[tex]\begin{gathered} \text{Angle of sector=}\frac{\phi}{360}\times\pi r^2 \\ \text{Where,} \\ r=14m \\ \phi=40^0 \\ \pi=3.14(\text{ but the answer has to be in terms of }\pi) \end{gathered}[/tex]On substitution, we will have the area of the sector as
[tex]\begin{gathered} \text{Area of shaded sector}=\frac{40}{360}\pi\times14^2 \\ \text{Area of shaded sector=}21.78\pi m^2 \\ \text{Area of shaded sector=21.78}\pi\text{m}^2 \end{gathered}[/tex]Therefore,
The area of the shaded sector in terms of π = 21.78πm²
