Answer:
[tex]2.9 cm^2[/tex]
Step-by-step explanation:
Given,
Angle of sector = 30°
Radius of circle, r = 8 cm
Area of the shaded region, A =?
The diagram is attached below.
Now,
Area of shaded region = Area of sector - Area of triangle
Area of triangle = [tex]\frac{1}{2}\times base \times height[/tex]
We know that,
[tex]\sin \theta = \dfrac{P}{H}[/tex]
[tex]\sin 30^\circ= \dfrac{P}{8}[/tex]
[tex]P = \dfrac{8}{2}[/tex]
[tex]P = 4\ cm[/tex]
And
[tex]\cos \theta =\dfrac{B}{H}[/tex]
[tex]\cos 30^\circ = \dfrac{B}{8}[/tex]
[tex]B = \dfrac{8\times \sqrt{3}}{2}[/tex]
[tex]B = 4\sqrt 3[/tex]
Area of sector = [tex]\dfrac{\theta}{360^\circ}\times \pi r^2[/tex]
Area of sector = [tex]\dfrac{30^\circ}{360^\circ}\times \pi \times 8^2[/tex]
= 16.75 cm^2
Area of triangle = [tex]\dfrac{1}{2} \times 4\sqrt 3 \times 4[/tex]
= 13.85 cm^2
Area of shaded region = 16.75 - 13.85
= [tex]2.9 cm^2[/tex]
