Latest TCS Aptitude Question SOLUTION: Two equilateral triangles of side 12cm are placed one on top of another, such that a 6 pointed star is formed. If the 6 vertices lie on a circle, what is the area of the circle not

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Two equilateral triangles of side 12cm are placed one on top of another, such that a 6 pointed star is formed. If the 6 vertices lie on a circle, what is the area of the circle not enclosed by the star? (Give answer to the nearest square cm)

Asked In TCS (10 years ago)

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Read Solution (11) :

jaffreyhudson  (10 years ago)

dear m4 maths everyone solves the quetions and gives diffrent answers . Please check and display the correct answers only. Dont display the wrong answers. We are totally confused about the solutions given by differnt people.

Is this solution Helpfull? Yes (45) | No   

soumyadeep saha  (10 years ago)

answer is 68cm^2 approx

Is this solution Helpfull? Yes (16) | No (4)  

Akanksha verma  (10 years ago)

radius of circumcircle of equilateral triangle=a/root 3
area of equilateral triangle is=root 3/4 *(a)
so,area remaining=area of circle-(area of triangle of side 12 +3*area of triangle with side 4)
=3.14*(12/root 3)^2-(root 3/4*(12)^2+3*root 3/4*(4)^2)
=83.174

Is this solution Helpfull? Yes (7) | No (7)  

sayan saha  (9 years ago)

Altitude of the triangle = 3√2a = 3√2(12) = 63√
We know that centroid divides the altitude in the ratio 2 : 1 and 23(Altitude) = Circum radius
Circum radius = 23(63√)=43√
Area of the circle = πr2=3.14×(43√)2
Now the two triangles in the circle forms 12 small equilateral triangles with side 4. So their total area = 12×3√4a2 = 12×3√442
Area which is not covered by the equilateral triangles = 3.14×(43√)2 - 12×3√442 = 67.65 ≃68

Is this solution Helpfull? Yes (7) | No   

lucky  (10 years ago)

Area = area of circle -(area of whole triangle of side 12cm + 3*area of triangle of side 4cm )
radius of circle is 4 under root 3, area of equilateral triangle root3/4 side square
Ans =3.88cm^2

Is this solution Helpfull? Yes (2) | No (4)  

Geetanjali Patil  (10 years ago)

how did you get it??????

Is this solution Helpfull? Yes (2) | No   

lucky  (10 years ago)

soory i have made mistake in calculations,approach is correct but correct ans is 68 only

Is this solution Helpfull? Yes (2) | No (1)  

Raju Sharma  (10 years ago)

plzz explain soumyadeep saha

Is this solution Helpfull? Yes (1) | No   

lucky  (10 years ago)

81cm square

Is this solution Helpfull? Yes | No (3)  

Bipra Sarkar  (10 years ago)

explain soumyadeep(bacchan)

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Amit kumar yadav  (8 years ago)

the correct solution should be given by M4 maths only as different people have diff ans

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