Question

find the area of the blue shaded region. 150° 6 cm area =? cm² round to the nearest tenth

Explanation:

Step1: Find the area of the whole circle

The formula for the area of a circle is $A = \pi r^{2}$, where $r = 6$ cm. So $A=\pi\times6^{2}= 36\pi$ $cm^{2}$.

Step2: Find the central - angle of the blue - shaded sector

The central - angle of the non - shaded sector is $150^{\circ}$, and the total central - angle of a circle is $360^{\circ}$. So the central - angle of the blue - shaded sector, $\theta=360 - 150=210^{\circ}$.

Step3: Find the area of the blue - shaded sector

The formula for the area of a sector of a circle is $A_{s}=\frac{\theta}{360}\times\pi r^{2}$, where $\theta$ is the central - angle of the sector and $r$ is the radius of the circle. Substituting $\theta = 210^{\circ}$ and $r = 6$ cm, we get $A_{s}=\frac{210}{360}\times36\pi$.
$A_{s}=\frac{210\times36\pi}{360}=21\pi\approx 21\times3.14 = 65.94\approx65.9$ $cm^{2}$.

Answer:

$65.9$