# Area of a Hexagon...

• May 1st 2010, 01:13 AM
jazthaman
Area of a Hexagon...
Just a bit confused as to what to do with the following question involving a hexagon insribed in a circle, area/geometry isn't my strongest link in maths. (Wondering)

The question asks to find the area of the hexagon inscribed in the circle.
Like so:

http://jersey.uoregon.edu/~probs/bas...88_figure4.gif
NOTE: The Radius of the circle is 1cm in the question instead of 10cm.

Would really appreciate it if someone could briefly outline the steps and formulas involved in solving this question.

Cheers,
Jaz
• May 1st 2010, 02:24 AM
Debsta
Quote:

Originally Posted by jazthaman
Just a bit confused as to what to do with the following question involving a hexagon insribed in a circle, area/geometry isn't my strongest link in maths. (Wondering)

The question asks to find the area of the hexagon inscribed in the circle.
Like so:

http://jersey.uoregon.edu/~probs/bas...88_figure4.gif
NOTE: The Radius of the circle is 1cm in the question instead of 10cm.

Would really appreciate it if someone could briefly outline the steps and formulas involved in solving this question.

Cheers,
Jaz

The regular hexagon is made up of 6 equilateral triangles where each side is 1cm. So find the area of an equilateral triangle (hint: draw the perpendicular height and use Pythagoras' rule OR use trigonometry) and multiply by 6.
• May 1st 2010, 04:09 PM
jazthaman
Quote:

Originally Posted by Debsta
The regular hexagon is made up of 6 equilateral triangles where each side is 1cm. So find the area of an equilateral triangle (hint: draw the perpendicular height and use Pythagoras' rule OR use trigonometry) and multiply by 6.

Thanks for that, Debsta.

So basically I just use the following area formula for an equilateral triangle;
http://www.mathwords.com/a/a_assets/...%20formula.gif

With s being 1cm, and from there I just multiply the answer I get from using the formula by 6?
• May 1st 2010, 06:17 PM
Debsta
Quote:

Originally Posted by jazthaman
Thanks for that, Debsta.

So basically I just use the following area formula for an equilateral triangle;
http://www.mathwords.com/a/a_assets/...%20formula.gif

With s being 1cm, and from there I just multiply the answer I get from using the formula by 6?

Yes that's right.
• May 1st 2010, 06:59 PM
jazthaman
Quote:

Originally Posted by Debsta
Yes that's right.

Cheers.

And from there I just simply find the area of the circle, then I subtract the area of the hexagon from the area of the circle?

Which ends up being;
Area of circle = PieR^2 = Pie x 1^2 = 3.1415962654
Area of equilateral triangle = 1^2 square root 3 divided by 4 = 0.433012702
Total area of equilateral triangles = 0.433012702 x 6 = 2.598076211

Therefore, Total Area of Hexagon = 3.1415962654 - 2.598076211 = Final Answer

Is that correct? (Thanks for your help thus far)
• May 1st 2010, 07:18 PM
Debsta
Quote:

Originally Posted by jazthaman
Cheers.

And from there I just simply find the area of the circle, then I subtract the area of the hexagon from the area of the circle?

Which ends up being;
Area of circle = PieR^2 = Pie x 1^2 = 3.1415962654
Area of equilateral triangle = 1^2 square root 3 divided by 4 = 0.433012702
Total area of equilateral triangles = 0.433012702 x 6 = 2.598076211

Therefore, Total Area of Hexagon = 3.1415962654 - 2.598076211 = Final Answer

Is that correct? (Thanks for your help thus far)

What you've found is the area inside the circle but outside the hexagon (ie the 6 segments around the circumference).
Your original question just asked for the area of the hexagon, which is just the 2.59 (or more precisely 3 sqrt(3)/2).
Reread the original question to see what you want.
• May 1st 2010, 07:39 PM
jazthaman
Quote:

Originally Posted by Debsta
What you've found is the area inside the circle but outside the hexagon (ie the 6 segments around the circumference).
Your original question just asked for the area of the hexagon, which is just the 2.59 (or more precisely 3 sqrt(3)/2).
Reread the original question to see what you want.

Oh ok, thanks for clearing that up.

The question only just asks for the area of the hexagon inscribed in the circle.

Thanks for all your help, really appreciate it.