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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. (Ta - Mathematics

Sum

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).

 

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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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APPEARS IN

RD Sharma Class 10 Maths
Chapter 13 Areas Related to Circles
Exercise 13.4 | Q 50 | Page 65
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