Question 7.
Given:
BD = 18 cm
m∠BEC = 136 degrees.
Let's find the area of the shaded sector.
To find the area of the shaded sector, apply the formula:
[tex]\text{Area}=2(\frac{\theta}{360}\times\pi r^2)[/tex]
Where:
θ = 136 degrees
r is the radius
To find the radius, we have:
Diameter, BD = 18 cm
Radius = diameter/2 = 18cm/2 = 9 cm
Now, substitute values into the formula and solve for the area.
[tex]\begin{gathered} \text{Area}=2(\frac{136}{360}\times\pi\times9^2) \\ \\ \text{Area}=2(\frac{136}{360}\times\pi\times81) \end{gathered}[/tex]
Solving further, we have:
[tex]\begin{gathered} Area=2(0.378\pi\times81) \\ \\ \text{Area}=2(96.13) \\ \\ \text{Area}=192.27cm^2 \end{gathered}[/tex]
Therefore, the area of the shaded sector is 192.27 square cm.
ANSWER:
192.27 cm²
