Math Help Forum: 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.

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


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

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.

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


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.

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;


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

Originally Posted by jazthaman

Thanks for that, Debsta.

So basically I just use the following area formula for an equilateral triangle;


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

Yes that's right.

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)

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.

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.