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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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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.

is an equilateral triangle
Likewise,

Here, an equilateral

is formed in each sector outside the circle and all the triangles formed inside the sector are equilateral.

Area of the resultant figure

Area of equilateral triangle
We know the area of an equilateral triangle of side

will be

The required area

Therefore, the area of the resulting figure will be

square units.
Hence,the correct answer is option 3)

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