Student Question

# How to program the polygon area formula on a Ti 84 Plus/Ti 84 calculator?I have scanned the internet for instructions on how to program the polygon area formula on a calculator, but I haven't had any success. If you know how to or have seen a youtube video on how to do it, please answer with the link or instructions.Thanks

PRGM New RPOLY

Prompt NPrompt L
Disp L^2N/4/tan(180/N)

That's it.  If you are using radians use pi instead of 180 in the above program.

N is the number of sides L is the side length.

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0->Sdim(L1)->N
FOR(I,1,N-1)
0->T
FOR(J,I+1,N)
T+L2(J-1)->T
S+L1(I)L2(J)sin(T)->S
End
End
S/2->S
Disp S

I think this one will work.  Please try it.  I tried it on regular polygons, but if you have a solved irregular polygon see if that works.  You must not put in the last side.  So if you have a 5 sided polygon, put in the first 4 sides.  You put the side lengths in L1 and Exterior Angles in L2.  You could use degree's or radians but make sure you are in the right angle mode.

Please tell me if it works.

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You can find the area by two methods.

1) you know the coordinates of the corners of the polynomials.  You then use the following formula

`A = 1/2 sum_(i=0)^(n-1) x_iy_(i+1)-x_(i+1)y_i`

`x_n = x_0` and `y_n = y_0`

This is the formula that I programmed.

2) if you know the length of the sides `(a_1, a_2, ... ,a_n)` and their exterior angles `(theta_1, theta_2, ..., theta_n)` you can use the following formula:

` A = 1/2 sum_(i=1)^(n-2) (a_i(sum_(j=i+1)^(n-1)a_jsin(sum_(k=1)^(j-1) theta_k)))`

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The x values go into L1 and the corresponding y values go int L2.  The values must be in counter clockwise order.  This is why you are getting the invalid dim message.

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Did my message help?

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The - is the minus sign.  You did get L1 by pressing the 2nd, STAT (List) button?

If you get invalid dim, you need to put some values into L1 and L2 (STAT Edit).

Hope that helps.

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You put the points in L1 they should be arranged counter clockwise.  If you put them in clockwise you will get -1*Area.  I tested it a couple of times, and it works.

Press PRGM goto New and enter POLYGON (or what you want)

Hit Enter

:dim(L1)->N
:0->S
:For(I,1,N-1)
:L1(I)L2(I+1)-L1(I+1)L2(I)+S->S
:End
:L1(N)L2(1)-L1(1)L2(N)+S->S
:S/2->S
:Disp S

You put the x values in L1 and y values in L2.  L1 and L2 are list variables from the 2nd STAT (LIST) functions.  -> is sto.  You get dim( from the 2nd STAT (LIST) ops list, For and End from the PRGM list, and DISP from PRGM I/O list.  I hope you have entered a program before or it might be kind of difficult, if not this should be easy.