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Question
In the following figure, ABC is an equilateral triangle of side 8 cm. A, B and C are the centres of circular arcs of radius 4 cm. Find the area of the shaded region correct upto 2 decimal places. (Take π =3.142 and`sqrt3` = 1.732).
Solution
Area of the shaded region can be calculated as shown below,
Area of the shaded region = Area of equilateral triangle − 3` xx`area of circular arc
`"∴ Area of the shaded region"=sqrt3/4xx8xx8-3xx60/360xxpixx4xx4`
`"∴ Area of the shaded region"=sqrt3xx2xx8-3xx1/6xxpixx4xx4`
`"∴ Area of the shaded region"=sqrt3xx16-1/2xxpixx16`
`"∴ Area of the shaded region"=sqrt3xx16-pixx8`
Substituting sqrt`3=1.732` and `pi=3.142`we get,
`"∴ Area of the shaded region"=1732xx16-3.142xx8`
`"∴ Area of the shaded region"=27.712-25.136`
`"∴ Area of the shaded region"=2.576`
Therefore, area of the shaded region is `2.576 cm^2`
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