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Please help with geometry

Please help with geometry-example-1
User Kinzleb
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1 Answer

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It's a equilateral triangle. The area of the white region is the area of a sector minus the area of a triangle.

(60^o)/(360^o)=(1)/(6)
The sector is 1/6 of the circle, therefore the area of the sector is 1/6 of area of the circle.
The formula of an area of the circle:
A_O=\pi r^2

The area of the sector:

A_s=(1)/(6)\cdot\pi\cdot12^2=(1)/(6)\pi\cdot144=24\pi\ m^2
The formula of an area of the equilateral triangle:
A_\Delta=(a^2\sqrt3)/(4)

A_\Delta=(12^2\sqrt3)/(4)=(144\sqrt3)/(4)=36\sqrt3\ m^2

The area of the segment:

A_(sg)=A_s-A_\Delta\to A_(sg)=(24\pi-36\sqrt3)m^2

The area of the shaded region:

A=A_O-A_(sg)\to A=144\pi-(24\pi-36\sqrt3)=144\pi-24\pi+36\sqrt3\\\\=\boxed{A=(120\pi+36\sqrt3)m^2}

User Channaveer Hakari
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