Trapezoid Midsegment, Height, Area

[Eddie W. Shore]

The program TRAPEZ calculates the following:

Midsegment length: M = (A + B)/2

Height: H = √( (-A+B+C+D)(A-B+C+D)(A-B+C-D)(A-B-C+D) )/(2 * abs(B-A))

Area: K = M * H

HP Prime Program TRAPEZ

Code:


EXPORT TRAPEZ()
BEGIN
// trapezoid
// 2017-06-23 EWS

INPUT({A,B,C,D},
"Trapezoid",
{"a: ","b: ","c: ","d: "},
{"Top","Bottom","Left","Right"});

M:=(A+B)/2;
I:=(−A+B+C+D)*(A-B+C+D)*(A-B+C-D)*
(A-B-C+D);
IF I≤0 THEN
PRINT();
PRINT("Invalid Trapezoid");
ELSE
H:=√(I)/(2*ABS(B-A));
K:=H*M;
PRINT();
PRINT("Midlength = "+M);
PRINT("Height = "+H);
PRINT("Area = "+K);
END;

END;

Example

A = 13, B = 23, C = 6, D = 7
Results:
Midlength, M = 18
Height, H = 4.139493194
Area, A = 74.3848775

Source:
“Trapezoid” Wikipedia. Edited July 7, 2014. Retrieved July 8, 2014
Current page:

[PedroLeiva]

(06-24-2017 02:32 AM)Eddie W. Shore Wrote:  The program TRAPEZ calculates the following:

Midsegment length: M = (A + B)/2

Height: H = √( (-A+B+C+D)(A-B+C+D)(A-B+C-D)(A-B-C+D) )/(2 * abs(B-A))

Area: K = M * H

HP Prime Program TRAPEZ

Code:


EXPORT TRAPEZ()
BEGIN
// trapezoid
// 2017-06-23 EWS

INPUT({A,B,C,D},
"Trapezoid",
{"a: ","b: ","c: ","d: "},
{"Top","Bottom","Left","Right"});

M:=(A+B)/2;
I:=(−A+B+C+D)*(A-B+C+D)*(A-B+C-D)*
(A-B-C+D);
IF I≤0 THEN
PRINT();
PRINT("Invalid Trapezoid");
ELSE
H:=√(I)/(2*ABS(B-A));
K:=H*M;
PRINT();
PRINT("Midlength = "+M);
PRINT("Height = "+H);
PRINT("Area = "+K);
END;

END;

Example

A = 13, B = 23, C = 6, D = 7
Results:
Midlength, M = 18
Height, H = 4.139493194
Area, A = 74.3848775

Source:
“Trapezoid” Wikipedia. Edited July 7, 2014. Retrieved July 8, 2014
Current page:

Hello Eddie, my calculations with Excel give me H=413,249319, just a 2 instead of 9

[SlideRule]

(06-24-2017 02:32 AM)Eddie W. Shore Wrote:  ... TRAPEZ calculates ... Area = [(A + B)/2] * [√( (-A+B+C+D)(A-B+C+D)(A-B+C-D)(A-B-C+D) )/(2 * abs(B-A))]

Another equation for the area when the only givens of a trapezoid are the four sides (a,b,c,d);
[attachment=4985]

BEST!
SlideRule

[StephenG1CMZ]

It may be worth pointing out that a trapezoid is one of those words whose meaning varies regionally...so one always needs to know (or guess) which trapezoid is which.

https://english.stackexchange.com/questi...ped-around