Thread: how to create any shape from an area

Hey all,

I usually don't deal with heavy maths on a regular basis so the way I communicate this may not be spot on, but here goes.

I wish to create shapes of ANY number of sides that have a specific area and I know the area of which they have to be.

For example, the area is 9cm squared, so to create a square shape from that I would squareroot it to find the length and breadth in order to draw the shape. I can also manage to do the same for a triangle by reversing (1/2(bxh)), but the shapes I want to draw are:

Semicircle - (I think i can do this one)
Heptagon - 7sides
dodecagon - 12 sides
hexadecagon - 16sides
icosagon - 20 sides

Any ideas how I create these shapes that have specific areas?


Thanks very much in advance,
Dave

There is a formula you can use for the area of a regular polygon.

. Where n is the number of sides.

For instance, for the septagon(7 sides), say you want an area of 20 square units:



Solve the radius and we get

Then, a side length would be

I've known these formulas for sometime, but here's a link to a useful site.

Regular Polygons - Properties

Here is another link that may help.
Regular Polygon -- from Wolfram MathWorld

excellent thanks.

Not being fluent with advanced maths, how would I type this into a calculator to work it out. (step by step)

I have no idea what r2 is.

Thanks.
Dave

I mentioned it in my first post. r is the radius, so r^2 is the radius squared.

ahh right, now I see.


Thanks alot.
Topic closed I guess.

Originally Posted by plastiman

excellent thanks.

Not being fluent with advanced maths, how would I type this into a calculator to work it out. (step by step)

I have no idea what r2 is.

Thanks.
Dave

This is not advanced math, just some trig and algebra. Though, I suppose it may seem that way.

Some calculators have solver functions. Such as a TI-89, TI-92, Voyage 200, etc. To do it algebraically, the old-fashioned way we may proceed as such:



Multiply both sides by 2/7:



Divide by :



Square root of both sides:



See?.

Here's a screen capture from the solve function in my TI-92.

As you can see, it easily solves for r.

It gives two solutions, but only one is viable because the other is negative.