Casio fx-CG 50 and HP
Prime: Pyramid Constructed by Points
The program PYRAPTS calculates the surface area and volume
of a pyramid that is defined by its vertex points. The program assumes all the points of its
base lies on the plane z = 0, and there is only one tip point.
All of the base points, B1, B2, B3, B4, etc., are entered as
two coordinates, one list for the X coordinates and the other for the
corresponding Y coordinates. Keep in
mind that for this program, all of its base points lie on the plane Z=0.
The coordinates for the tip point, T, are prompted
separately.
Casio fx-CG 50 Program PYRAPTS (text file)
'ProgramMode:RUN
"2018-06-24
EWS"
ClrText
Red Locate
1,1,"FOR THE BASE, Z=0"
For 1->J To 1000
Next
"X _List
_"?->List 1
"Y _List
_"?->List 2
Dim List 1->N
"TIP X
COORD="?->X
"TIP Y
COORD="?->Y
"TIP Z
COORD="?->Z
0->S
List 1[1]*List
2[N]-List 1[N]*List 2[1]->R
For 2->J To N
R+List 1[J]*List
2[J-1]-List 1[J-1]*List 2[J]->R
Sqrt(Z^<2>+(Y-List
2[J])^<2>+(X-List 1[J])^<2>)->A
Sqrt(Z^<2>+(Y-List
2[J-1])^<2>+(X-List 1[J-1])^<2>)->B
Sqrt((List 2[J]-List
2[J-1])^<2>+(List 1[J]-List 1[J-1])^<2>)->C
(A+B+C)/2->H
S+Sqrt(H(H-A)(H-B)(H-C))->S
Next
Abs R/2->R
S+R->S
RZ/3->V
ClrText
Blue Locate
1,1,"SURFACE AREA="
Red Locate 1,2,S
Blue Locate
1,4,"VOLUME="
Red Locate 1,5,V
Notes:
1. - > is the storage arrow →
2. ^<2> is the
square key x^2
3. If you type in the
program manually, the line ‘ProgramMode:RUN is not needed
4. _ represents the
space key
HP Prime Program PYRAPTS
EXPORT
PYRAPTS()
BEGIN
//
2018-06-25 EWS
//
pyramid by points
LOCAL
L1,L2,X,Y,Z;
LOCAL
S,V,R,J,N;
INPUT({{L1,[[6]]},
{L2,[[6]]}},"Base
Points: Z=0",
{"X
List:","Y List:"});
N:=SIZE(L1);
INPUT({X,Y,Z},"Tip
Coordinates",
{"X:
","Y: ","Z: "});
S:=0;
R:=L1(1)*L2(N)-L1(N)*L2(1);
FOR
J FROM 2 TO N DO
R:=R+L1(J)*L2(J-1)-L1(J-1)*L2(J);
A:=√(Z^2+(Y-L2(J))^2+
(X-L1(J))^2);
B:=√(Z^2+(Y-L2(J-1))^2
+(X-L1(J-1))^2);
C:=√((L2(J)-L2(J-1))^2
+(L1(J)-L1(J-1))^2);
H:=(A+B+C)/2;
S:=S+√(H*(H-A)*(H-B)*(H-C));
END;
R:=ABS(R)/2;
S:=S+R;
V:=R*Z/3;
PRINT();
PRINT("Surface
Area: "+S);
PRINT("Volume:
"+V);
RETURN
{S,V};
END;
Example
Base points:
(0,0,0), (3,4,0), (-3,4,0)
(z=0 is implied for base points)
Tip point: (0,1,√2)
Input:
List X: {0, 3, -3}
List Y: {0, 4, 4}
Tip X: 0
Tip Y: 1
Tip Z: √2
Results:
Surface Area: 25.7904472451
Volume: 5.65685424947
Eddie
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content copyright, © 2011-2018. Edward
Shore. Unauthorized use and/or
unauthorized distribution for commercial purposes without express and written
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