Latest TCS Aptitude Question SOLUTION: Two equilateral triangles of side 12 units are drawn one upon the other to form a star and a common circum circle is drawn to them then finds the area enclosed in circle but not in

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Two equilateral triangles of side 12 units are drawn one upon the other to form a star and a common circum circle is drawn to them then finds the area enclosed in circle but not in star.

Asked In TCS rajendra prasad (9 years ago)

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Surit Datta  (9 years ago)

According to the question,
area of the equilateral triangles are sqrt(3)*a*a/4
here a is 12 units
so the area of the triangle is 36*sqrt(3) sq.units
now the radius of the circle is s/sqrt(3)
where s is the side of the equilateral triangle
which is 12 units.
so radius is 12/sqrt(3) units.
so area of the circle is pi*(12/sqrt(3))^2
which is 48*pi sq.units.
now in between those two triangle a hexagon is formed,
whose side is 12/3 = 4 units,
so the area of the hexagon is 3*sqrt(3)*4*4/2 = 24*sqrt(3) sq.units....according to the formula
now the area of the circle leaving the area of the star is,
48*pi - (24*sqrt(3)+24*sqrt(3)) sq.units
which is 48*(pi - sqrt(3)) sq.units.
I am not sure about the solution.
Correct me if i am wrong.

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SOURAV SAHA  (9 years ago)

i think ans will be 12pi unit^2.

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Rounak Lahoti  (9 years ago)

length of median of equi. triangle=a(root[3]/2)
pi(6*root[3])^2-(root[3])/4(12)^2 ans

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