I need to solve this but I don't know how..
Please help me with this one..

A regular hexagon with an area of 93.53 sq. cm. is inscribed in a circle. Find the area not covered by the hexagon. Sketch the figure and solve.

Question

I need to solve this but I don't know how..
Please help me with this one..

A regular hexagon with an area of 93.53 sq. cm. is inscribed in a circle. Find the area not covered by the hexagon. Sketch the figure and solve.

anonymous · Answer

@Directrix help me.. please?????

anonymous · Answer

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is you can find the length of this (which is the same length as any 1 side of the haxagon)  you have the radius of the circle meaning you can find the area of the circle.

Area you want = Area Circle - Area Hexagon

anonymous · Answer

|dw:1385169948197:dw|

directrix · Answer

@CUTESE7EN

I will help you with this if you stay "live" on this thread and work with me.

Do we have a deal?

anonymous · Answer

okay :) I will. :) thanks..

directrix · Answer

Okay. Let's roll. First, I will upload the image of a regular hexagon inscribed in a circle.

anonymous · Answer

okay. :) then?

directrix · Answer

The central angle measures are each 60. That comes from 360/60 = 6.

Look at one of the six triangles.

Radii of the same circle are congruent so two sides of the triangle are congruent.

Because the vertex angle is 60 and base angles of an isosceles triangle are congruent, the triangle is equilateral and equiangular. 

Study through that and see if you agree.

anonymous · Answer

ahh.. :) the hexagon has 6 equilateral triangles.. then?

directrix · Answer

The area of the regular hexagon is given to be 93.53. 

Each of the 6 equilateral triangles that make up the regular hexagon are congruent.

Therefore, each of the 6 equilateral triangles has the same area.

Your Task: Find the area of ONE of the 6 triangles by dividing 93.53 by 6.

Post what you get.

anonymous · Answer

15.5833333 :)

directrix · Answer

Okay.  

What we are about to do is to find the radius of the circle. With it, we can get the area of the circle and then subtract the given area of the regular hexagon and get the area inside the circle but outside the hexagon.

directrix · Answer

Because the radius of the circle is the same as a side of the equilateral triangle AND the area of the equilateral triangle is 15.588 approx, we will use a "speciality" formula for the area of the triangle and solve for the side of the triangle which is also the radius of the circle.

directrix · Answer

We have to solve this equation for s, where s is the side of the triangle and also the radius of the circumscribed circle.


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