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Sagot :
First, let's find the area circular sector:
[tex]A=\frac{r^2\theta}{2}[/tex]Where:
r = radius = 7cm
θ = angle (in radians) = 5/6 π
so:
[tex]\begin{gathered} A=\frac{7^2(\frac{5}{6}\pi)}{2} \\ A=\frac{245}{12}\pi \end{gathered}[/tex]Now, let's find the area of the triangle, that triangle is an isosceles triangle, so, we can use the following formula in order to find its area:
[tex]\begin{gathered} At=\frac{1}{2}s^2\cdot\sin (\theta) \\ \end{gathered}[/tex]where:
s = one of the equal sides = 7
θ = angle = 150
so:
[tex]\begin{gathered} At=\frac{1}{2}(7^2)\sin (150) \\ At=\frac{49}{4} \end{gathered}[/tex]Therefore, the area of the white region will be, the area of the circular sector minus the area of the isosceles triangle, so:
[tex]Area_{\text{ }}of_{\text{ }}the_{\text{ }}white_{\text{ }}region=\frac{245}{12}\pi-\frac{49}{4}=51.9cm^2[/tex]
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