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Q.

A circle of radius ‘a’ is divided into 6 equal sectors. An equilateral triangle is drawn on the chord of each sector to lie outside the circle. Area of the resulting figure is:


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a

Question Image

b

Question Image

c

Question Image

d

None of these 

answer is C.

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Detailed Solution

Concept- The area of an equilateral triangle is indeed the amount of space it takes up in a two-dimensional plane.
As per the given information, we can draw the figure.
imageQuestion Image is an equilateral triangle
Likewise, Question ImageHere, an equilateral Question Image is formed in each sector outside the circle and all the triangles formed inside the sector are equilateral.
Question ImageArea of the resultant figure Question Image Area of equilateral triangle
We know the area of an equilateral triangle of side Question Image will be Question Image.
Question ImageThe required area Question ImageQuestion ImageTherefore, the area of the resulting figure will be Question Image square units.
Hence,the correct answer is option 3) Question Image.
 
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