Question

Mathematicians come thru wit da help

Answer 1

Answer:

$A=7\pi\ cm^2-\frac{343}{6}\ cm^2$

Step-by-step explanation:

Area of plane figures

Being r the radius of a circle, the area of a sector defined by an angle $\theta$ is

$A_s=\frac{\theta}{2} r^2$

If a is the repeated side of an isosceles triangle and $\beta$ is the angle they define, then the area of the triangle is

$A_t=\frac{a^2}{2}sin\beta$

The figure shows a circle with radius of r=7 cm. The white area is equal to the area of the circle minus the blue area

The area of the circle is

$A_c=\pi r^2=49\pi cm^2$

The blue area is the sum of the sector defined by the angle (360-150)=$210^o$ and the triangle. An angle of $210^o$ is equivalent to

$\frac{\pi}{180^o}210^o=\frac{7}{6}\pi$

The area of the sector is

$A_s=\frac{7}{12}\pi (7^2)=\frac{343\pi}{12}\ cm^2$

The area of the triangle with center angle 150^o is

$A_t=\frac{(7)(7)}{2}sin150^o$

$A_t=\frac{49}{2}\frac{1}{2}$

$A_t=\frac{49}{4}\ cm^2$

The blue area is

$\frac{49}{4}\ cm^2+\frac{343}{12}\pi\ cm^2$

Finally, the white area is

$A=49\pi cm^2-(\frac{49}{4}\ cm^2+\frac{343}{12}\pi\ cm^2)$

$A=\frac{245}{12}\pi\ cm^2-\frac{49}{4}\ cm^2$