rishabhmishra wrote:

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

Attachment:

The attachment **Screenshot (72).png** is no longer available

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

\(24\sqrt{3}\)

Attachments

InkedScreenshot (72)_LI.jpg [ 806.94 KiB | Viewed 373 times ]