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(#M40038222) ELITMUS Numerical Ability question Keep an EYE

an equilateral triangle of side 18cm is cut and a regular hexagon of the lagrest possible side is carved out of it. find the area of hexagon.

Asked In Elitmus Liti (11 years ago)

Unsolved Read Solution (15)

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Read Solution (15) :

Pradeep  (11 years ago)

54 sqrt (3) as equliateral triangle side =18cm divide this side into 3 equal parts =18/3=6 ;; area of hexagon = 3*sqrt(3) /2 (side)^2 =3*sqrt(3)/2 (6)^2 = 54 sqrt(3)

Is this solution Helpfull? Yes (14) | No (7)  

Pravena  (11 years ago)

An equilateral triangle of side 18cm is cut and a regular hexagon of the lagrest possible side is carved out of it. find the area of hexagon
A. 120.5√3
B. 123.5√3
C. 121.5√3
D. 124.5√3

solution
Perimeter of hexagon=Perimeter of triangle
6a=3a
6a=3*18
a=9
area of hexagon = 6*(√3/4)a^2
=121.5√3

Is this solution Helpfull? Yes (13) | No (1)  

Neera Aggarwal  (11 years ago)

Perimeter of Hexagon= 6a
6a=18x3
a=9

Area of Hexagon= (3)((3)^1/2)(a^a)/2 = (3^5)(3^1/2)/2

Is this solution Helpfull? Yes (12) | No (15)  

pranav khandelwal  (11 years ago)

Dear Pradeep,
18 cm is length of one side According to your solution there will be nine sides in hexagon.please elaborate further
Now,
Perimeter of triangle=54
thus one side's length=54/6=9cm
thus area=243sqrt(3)/2

Is this solution Helpfull? Yes (6) | No (2)  

Pradeep  (11 years ago)

93.53 or= 54 Sqrt 3.

Divide the side into three equal parts and fold the triangle at the three corners.

Area = (3 Sqrt 3 * 6)/2 = 54 Sqrt 3

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Dipanjan Dasgupta  (11 years ago)

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The required figure takes this shape

For a regular hexagon of the largest possible side to fit inside an equilateral triangle length of each side of the hexagon must be equal to 1/3rd length of the
side of the equilateral triangle.

So, length of each side of the hexagon is 18/3 = 6cm.

Area of the hexagon = 0.433*side*side = 0.433*6*6 = 15.59

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

Dipanjan Dasgupta  (11 years ago)

I created the figure 4 this question, but after posting my answer all the sequence of the diagram got disturbed, so the diagram did not come clearly....

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raj  (11 years ago)

formula for hexagon from equilateral triangle is 6*(sqrt(3)/4)*side_square

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Anjali kumari  (9 years ago)

here given side of equilateral triangle=18cm
let side of hexagon=acm
perimeter of hexagon=perimeter of euilateral traingle
6a=3*side of traingle
6a=3*18
a=9cm
area of hexagon =3*sqrt(3)/2 *(side)^2
=3*sqrt(3)/2 *(9)^2
=121.5sqrt(3)
ans c

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priyanka bisht  (11 years ago)

plzzz..pradeep explain in detail..

Is this solution Helpfull? Yes | No (1)  

veer kumar  (11 years ago)

the largest possible polygon from the triangle will be drawn inside the incircle
of the given triangle.
now the area of incircle of an equilateral triangle of side X is (pi/12)*x^2
=> radius of incircle =sqrt(27)=3*sqrt(3)
now if we will draw the hexagon within this circle then each side will be equal to 3*sqrt(3) now if we join the all the vertices of the hexagon through diagonals of hexagon then we will get 6 equilateral triangle of side 3*sqrt(3)
=>area of 1 triangle = (sqrt(3)/4)*(3*sqrt(3))^2=(27*sqrt(3))/4
area of 6 triangle = area of hexagon=6*(27*sqrt(3))/4=(81*sqrt(3))/2=70.148

Is this solution Helpfull? Yes | No (2)  

arjun kumar jha  (11 years ago)

u can use direct formula.here..formula to find out area of regular polygons is.. n*s^2/4*cot(180/n)..where....n=no of side.and s= length of side....
in this question n=6 and side length is 54/6=9. so area==6*9*9/4 * cot(180/6) it results in......81*6(root 3)/4...!

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Dipanjan  (10 years ago)

AREA OF A EQUILATERAL TRIANGLE= SQRT(3)*(SIDE)^2/4.
AREA=SQRT(3)*(18)^2/4
AREA OF LARGEST REGULAR HEXAGON =6* SQRT(3)*(18)^2/4. [as a regular hexagon comprises of 6 equilateral triangles]
AREA=486*SQRT(3).

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SUBRATA SARKER  (10 years ago)

perimeter of hexagon= 18*3= 54
side of hexagon= 54/6= 9
area of hexagon= [{3* sqrt(3)} /2] * 9^2 ]

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kundan prasad  (10 years ago)

Ans:c)121.5/cub root(3)
Sol:
Formula for Area of Equilateral triangle =cub root(3)*a*a/4 where a is length of Equilateral triangle
Area of triangle is =cub root(3)*18*18/4=4.5*3/cub root(3) cm^2
Area of hexagon=6*cub root(3)*b*b/4 where b is side of hexagon
largest area is carved out of it =Area of triangle - Area of Hexagon
=4.5/cub root(3-b*b) cm^2
check the of option should be divisible by 4.5/cub root(3)
we get option c

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