1 Answer

Kelu Thatsall · Answer 1 · 2020-10-07T15:09:38+0000

Answer:

$A=7\pi\ cm^2-(343)/(6)\ cm^2$

Explanation:

Area of plane figures

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

$A_s=(\theta)/(2) r^2$

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

$A_t=(a^2)/(2)sin\beta$

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

$(\pi)/(180^o)210^o=(7)/(6)\pi$

The area of the sector is

$A_s=(7)/(12)\pi (7^2)=(343\pi)/(12)\ cm^2$

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

A_t=((7)(7))/(2)sin150^o

A_t=(49)/(2)(1)/(2)

$A_t=(49)/(4)\ cm^2$

The blue area is

$(49)/(4)\ cm^2+(343)/(12)\pi\ cm^2$

Finally, the white area is

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

$A=(245)/(12)\pi\ cm^2-(49)/(4)\ cm^2$

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