Latest TCS Aptitude Question SOLUTION: Two equilateral triangles of sides 12cms are placed one on top of another,such that a six pointed star is formed. If the six vertices lie on the circle,what is the area of the circ

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Two equilateral triangles of sides 12cms are placed one on top of another,such that a six pointed star is formed. If the six vertices lie on the circle,what is the area of the circle not enclosed by the star?

Asked In TCS MOUNIKA (10 years ago)

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Ashutosh verma  (10 years ago)

ans 48(pi-root3)
area of 1 triangle= ((root3)/4)*12^2
area of small triangle=((root3)/4)*4^2
radius of circle = 12/ root3
area not covered= pi(12/ root3)-(((root3)/4)*12^2+3*((root3)/4)*4^2)

Is this solution Helpfull? Yes (12) | No (1)  

Naveenprabhu  (10 years ago)

Eq. tri Area= side2*√3/4
Given Side=12 cm
One eq.triangle placed over other they cut the line in ratio 1:3
Side of smaller triangle=12/3=4 cm
Total area covered by two triangles= ( (12*12)+3(4*4))*√3/4
=48√3
Radius of circle=side/√3=12/√3
Area of Circle=A=πr^2=48π
Uncovered area=48(π-√3)

Is this solution Helpfull? Yes (9) | No (1)  

swati  (10 years ago)

common part of two triangle is hexagon so from he center of the circle draw 6 triangle in hexagon. so total there is equilateral 12 triangle after that their find altitude of one of the main triangle that is (sqrt(3)/4)*(a*a)=1/2 * 12(base) * altitude
so altitude is=6sqrt(3)
now the small triangle below that altitude having the altitude is (sqrt(3)/4)*(a*a) where a=4 because all 12 triangle is equilateral = 1/2 * 4(base) * altitude
sp altitude=2sqrt(3)
so diameter of circle=6sqrt(3) + 2sqrt(3) = 8sqrt(3) so radius is = 4sqrt(3)
remaining area (ans) = pi * r * r – 12* (sqrt(3)/4) * a * a where a=4
so ans is=67.58

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way  (10 years ago)

48(pi-root3)

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way  (10 years ago)

12(4pi-root3)

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Chandra Bhatt  (10 years ago)

72pi-120(sqrt3)=18.348 cm sqr.

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subhrajit mitra  (10 years ago)

area of 1 triangle= ((root3)/4)*12^2=62.352
area of small triangle=((root3)/4)*4^2=6.928
radius of circle= ((root3)/2)*12*3/4=9*(root3)/2=7.794
area of circle= pi*(7.794)^2=216.86
ans will be=216.86-(62.352+3*6.928)=133.724

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kumud kumari  (10 years ago)

answer is 152.064cmsq

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