Hey UG.

If I have 1000 m, and I need to construct these shapes

Octagon
10 sided shape
50 sided shape
100 sided shape

And the 1000 m is used to make each side of the perimeter EQUAL (as in divided up equally), what would the areas be of these shapes?

R E G G A E
Last edited by TheDarkestNights at Feb 7, 2007,
8000m
10,000m
50,000m
100,000m

?
Well, gimme half an hour.
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oh yeah? well larry king the slayer guitarist owns bc rich guitars. (i think)
Quote by TheDarkestNights
Hey UG.

If I have 1000 m, and I need to construct these shapes

Octagon
10 sided shape
50 sided shape
100 sided shape

And the 1000 m is used to make each side of the perimeter EQUAL (as in divided up equally), what would the areas be of these shapes?

do you mean that the shapes perimiters will add up to 1000m?

so eachwill have a perimiter of 250m?
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do you mean that the shapes perimiters will add up to 1000m?

so eachwill have a perimiter of 250m?

No, a perimiter of 1000m each.

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OK.

Each of these shapes will have a perimeter of 1000 metres. They are all regular. I need the areas. Ask if you need anything else.
R E G G A E
Divide the inside into triangles and calculate the area of 1 triangle.
Area * amount of sides = solution

It's prolly something along those lines.
Curiosity got the better of me...when will you ever need to be able to do anything like that ever in your life?

That, my friends, is why I hated maths.
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Quote by cagnius
Curiosity got the better of me...when will you ever need to be able to do anything like that ever in your life?

That, my friends, is why I hated maths.

No you won't, but homework's a motherf*cker.
R E G G A E
Quote by cagnius
Curiosity got the better of me...when will you ever need to be able to do anything like that ever in your life?

That, my friends, is why I hated maths.

It reflects your ability to solve problems. Just because it doesn't have a practical application (even though this does, if you're going to be something like an engineer or architect), doesn't mean it isn't worthwhile doing.
Quote by TheDarkestNights
No you won't, but homework's a motherf*cker.

It sure is.

It got to the point that I wouldn't do the homework unless my (very cool and compassionate teacher) could explain to me when I would ever need it in the future.

I rarely did homework in Higher Maths...
Terms and Conditions apply.
You can divide an octagon in 8 equal triangles. 360 degrees/ 8 = 45 degrees. All corners of a triangle added up equal 180. (180 - 45) / 2 = 67,5. To use goniometry, you need a 90 degree corner. So you'll have to cut the triangle in half. 45/2 = 22,5 degrees. 1000/8/2 = 62,5.

The area of a triangle is the hight x half base, so we'll have to find out the hight of the triangle.

That'll be TAN 22,5 = 62,5/x. So x = 62,5/(TAN 22,5).

125 x 62,5/(TAN 22,5) x 0,5 = Area of 1/8 octagon.

Just multiply by 8.

Area of a regular octagon with a perimeter of 1000 metres = 74,840.62 square metres
Quote by lizarday
oh yeah? well larry king the slayer guitarist owns bc rich guitars. (i think)
Please guys, I need this quickly. Any ideas??

EDIT:
Area of a regular octagon with a perimeter of 1000 metres = 74,840.62 square metres

I love you.
R E G G A E
Donate me 5 euros and I'll draw it out in paint.
Quote by lizarday
oh yeah? well larry king the slayer guitarist owns bc rich guitars. (i think)
Let n be the number of sides in your shape.
Let x be the length of each side.

I'll use a 6 sided shape as an example, cos it's easier to draw

x = 1000/n

Imagine drawing a line from the centre to each corner, and from the centre to the idpoint of each side.

This will give you 2n triangles.

The length of the outer side of these triangles will be 1000/2n = 500/n.

The angle at the centre, Ø, will be 360/2n = 180/n.

Using tanØ = opposite / adjacent (rearrange to A = O/tanØ, you can work out the distance from the centre to the middle of each line.

The area of the shape is then given by opposite x adjacent x n.

Where opposite = 500/n and adjacent is (500/n)/tanØ.

Comprendé?

EDIT: drawing diagrams helps.

Double edit: damn I typed slow
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Last edited by FrenchyFungus at Feb 7, 2007,
Quote by FrenchyFungus
Let n be the number of sides in your shape.
Let x be the length of each side.

I'll use a 6 sided shape as an example, cos it's easier to draw

x = 1000/n

Imagine drawing a line from the centre to each corner, and from the centre to the idpoint of each side.

This will give you 2n triangles.

The length of the outer side of these triangles will be 1000/2n = 500/n.

The angle at the centre, Ø, will be 360/2n = 180/n.

Using tanØ = opposite / adjacent (rearrange to A = O/tanØ, you can work out the distance from the centre to the middle of each line.

The area of the shape is then given by opposite x adjacent x n.

Where opposite = 500/n and adjacent is (500/n)/tanØ.

Comprendé?

I love it when you talk dirty Frenchie
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I'm assuming you're doing some sort of coursework, since I did exactly the same thing for my GCSE coursework. You can have the formulae, if you like.

Formula (where n=number of sides):
Area = n*((1000/2n)*((1000/2n)/(tan(360/2n))))

And if you're using Excel to make a spreadsheet of it, you'll need to use Radians instead of normal degrees, which means using this forumla:
Area = n*((1000/2n)*((1000/2n)/(tan((360*PI()/180)/2n))))

Hope this helped.
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Quote by cagnius
Curiosity got the better of me...when will you ever need to be able to do anything like that ever in your life?

That, my friends, is why I hated maths.

Unlike history/geography/religious studies/ science etc where knowledge of the kings of early 18th century france/where ouagadougu is/why some people believe some stuff you dont/how many atoms there are in your shoelace (in that order) is immensely valueable knowledge that everybody should/must know in order to have a good life? Your ignorance does not mean the ability to do such things is unecessary.

Anywho, to the threadstarter, in general, to find the area of a regular n-gon (n-sided shape) when given the perimeter, you first find the side length of said n-gon (by dividing the perimeter by the number of sides) then find the size of the interior angles of the n-gon (there is a formula for this, i wont tell you it, but think how many sides a trianlge has, and what its interior angles add up to, then do the same for a square, pentagon etc and spot the pattern) then you must spot that each regular n-gon is made up of n isosceles triangles. since you know the length of one side of each triangle (the one that is the side of the n-gon) and the size of the equal angles in the isosceles triangle (half the size of the interior angles) you can find the area of one of the triangles. Simply multiply this value by n to find the are of the n-gon.
i swear its that easy.
Quote by porcupineoris
Unlike history/geography/religious studies/ science etc where knowledge of the kings of early 18th century france/where ouagadougu is/why some people believe some stuff you dont/how many atoms there are in your shoelace (in that order) is immensely valueable knowledge that everybody should/must know in order to have a good life? Your ignorance does not mean the ability to do such things is unecessary.

I wouldn't call it ignorance. I took the time to learn to do these things. I, however, used my personal choice to not do the homework as it would be of no use to me after doing that class. That's not ignorance, its personal choice.
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Quote by cagnius
I wouldn't call it ignorance. I took the time to learn to do these things. I, however, used my personal choice to not do the homework as it would be of no use to me after doing that class. That's not ignorance, its personal choice.

Bah, choice is overated. Like Steak and Kidney pie and the internet.
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Quote by cagnius
I wouldn't call it ignorance. I took the time to learn to do these things. I, however, used my personal choice to not do the homework as it would be of no use to me after doing that class. That's not ignorance, its personal choice.

I think feeling the need to question the use/importance of mathematics is a prime example of ignorance.