Find the Area of the Shaded Regionin the figure Below, Where a Circular arc of Radius 6 cm has been Drawn with vertex O of an Equilateral traingle OAB of side 12 cm as centre.

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Find the area of the shaded regionin the figure below, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral traingle OAB of side 12 cm as centre.







Here we can see that

Area of required figure = Area of circle+Area of triangle− Area of the sector

⇒A(circle)=`π"r"^2`

⇒A(circle)=`\pi` `6^2`

⇒A(circle)=36`\pi`

⇒A(triangle)=`\frac{\sqrt{3}}{4}a^2`

⇒A(triangle)=`\frac{\sqrt{3}}{4}(12^2)`

⇒A(triangle)= `36\sqrt{3}`

⇒A(sector)=`1/2``"r"^2``\theta`

⇒A(sector)=`1/2`(`"6"^2`)`\frac{\pi}{3}`

⇒A(sector)=6`\pi`


Therefore, Required Area=36`\pi` + `36 \sqrt{3}` − 6`\pi`

⇒ Required Area=36`\pi` + `36 \sqrt{3}`​

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