## Friday, June 6, 2014

### HP 15C: Area of a Polygon by Vertices (revised)

HP 15C: Area of a Polygon by Vertices (revised)

In December 2011, I posted a program to calculate the area of a polygon given the vertices for the HP 15C. You can find the original program here:

http://edspi31415.blogspot.com/2011/12/hp-15c-programming-tutorial-part-15.html

The problem with this, that the area is not accurate when the initial point is not (0,0). This was brought up by Jason Foose. Jason, a million thanks.

Here is another attempt at it, this time it should work with any initial point. I tested the program with several different polygons and so far, so good.

Please test and let me know what you think. The instructions remain the same:
1. Enter the initial y coordinate, press ENTER, then enter the initial x coordinate, and press [ f ] [ √ ] (LBL A).
2. For each additional point, enter the y coordinate, press ENTER, then enter the x coordinate, and finally [ f ] [ e^x ] (LBL B).
3. To calculate the area, press [ f ] [10^x ] (LBL C).

Memory registers used:
R0 = area
R1 = x_i
R2 = y_i
R3 = x_i+1
R4 = y_i+1
R5 = Σ (x_i * y_i+1) // ( i=1...n and cycle back to 1)
R6 = Σ (x_i+1 * y_i)
R7 = x_1
R8 = y_1

Program - HP 15C:
LBL A
0
STO 5
STO 6
R down \\ R↓
STO 1
STO 7
R down
STO 2
STO 8
RTN

LBL B // step 12
STO 3
RCL× 2
STO+ 6
R down
STO 4
RCL× 1
STO+ 5
RCL 4
STO 2
RCL 3
STO 1
RTN

LBL C // step 25
RCL 7
RCL× 2
STO+ 6
RCL 8
RCL× 1
STO+ 5
RCL 5
RCL- 6
ABS
2
÷
STO 0
RTN

Total: 38 steps

Eddie

This blog is property of Edward Shore. 2014