find the area of the blue shaded region. 130° 11.1 m area = ? m² round to the nearest tenth.

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector of a circle is $A=\frac{\theta}{360}\times\pi r^{2}$, where $\theta$ is the central - angle of the sector and $r$ is the radius of the circle.

Step2: Identify the values of $\theta$ and $r$

Here, $\theta = 130^{\circ}$ and $r = 11.1$ m.

Step3: Substitute the values into the formula

$A=\frac{130}{360}\times\pi\times(11.1)^{2}$ First, calculate $(11.1)^{2}=123.21$. Then, $\frac{130}{360}\times\pi\times123.21=\frac{130\times\pi\times123.21}{360}$. $130\times123.21 = 16017.3$, and $\frac{16017.3\pi}{360}$. Using $\pi\approx3.14$, we have $\frac{16017.3\times3.14}{360}=\frac{50294.322}{360}\approx139.7$.

Answer:

$139.7$ m²