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555-605 (Medium)|   Geometry|      
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rishabhmishra
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If each of the line segments in the figure above has a length equal to 14 Mar 2018, 00:54
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78% (02:05) correct 22% (01:49) wrong based on 76 sessions

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If each of the line segments in the figure above has a length equal to 4, and the angle a,b and c are each 60 degrees, what is the total area of the shaded figure?

A. 16
B. \(8\sqrt{3}\)
C. \(24\sqrt{2}\)
D. 36
E. \(24\sqrt{3}\)

Source :- globalexperts

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rishabhmishra
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rishabhmishra

If each of the line segments in the figure above has a length equal to 4, and the angle a,b and c are each 60 degrees, what is the total area of the shaded figure?

A. 16
B. \(8\sqrt{3}\)
C. \(24\sqrt{2}\)
D. 36
E. \(24\sqrt{3}\)

Source :- globalexperts

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If you look at the attached photo we divide the figure into triangles
SO if each side is 4 and a,b and c=60
then take one triangle lets take c triangle
2 sides are equal and one is 60 then 2 sides is also 60 as if we take both side as x then 2x+60=180
and that means 3rd side is also equal to 4
now we can say these things will true in all triangles and each triangle is equilateral triangle
so area of equilateral triangle is \(\sqrt{3}side^2/4\) (root3*sidesquare/ 4)
so\(\sqrt{3}*4^2*6(total triangles in the figure)/4\)
answer is
\(24\sqrt{3}\)
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If each of the line segments in the figure above has a length equal to 14 Mar 2018, 02:13
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rishabhmishra

If each of the line segments in the figure above has a length equal to 4, and the angle a,b and c are each 60 degrees, what is the total area of the shaded figure?

A. 16
B. \(8\sqrt{3}\)
C. \(24\sqrt{2}\)
D. 36
E. \(24\sqrt{3}\)

Source :- globalexperts

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Hi...
All three figures are parallelogram with side 4..
Just take one of them..
Draw a PERPENDICULAR from a point to get height of this llgm.
We get a 30-60-90 triangle where hypotenuse is 4..
So side opposite 60 will be \(\frac{√3*4}{2}=2√3\)
Area of that llgm =\(4*2√3=8√3\)

Area of all three llgms = \(3*8√3=24√3\)

E
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If each of the line segments in the figure above has a length equal to 13 Oct 2020, 03:56
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rishabhmishra

If each of the line segments in the figure above has a length equal to 4, and the angle a,b and c are each 60 degrees, what is the total area of the shaded figure?

A. 16
B. \(8\sqrt{3}\)
C. \(24\sqrt{2}\)
D. 36
E. \(24\sqrt{3}\)

Source :- globalexperts

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Since, all the sides are equal & each of the parallelograms has 60-120-60-120 angle measures, we can deduct that all of the 3 parallelograms must be Rhombuses.
Area of a Rhombus = (side)^2 * sin(any inscribed angle°)
so, Area of 1 Rhombus = 4^2* sin60° = 16*(√3/2)=8√3
Total Shaded Area = Area of 3 Rhombus = 3*8√3 = 24√3
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