(41C) Area of Triangle (SSS)

[Albert Chan]

(11-10-2018 03:22 PM)Albert Chan Wrote:  If the sides are sorted, a >= b >= c, Kahan's formula is more accurate.

(11-12-2018 01:32 AM)Albert Chan Wrote:  Let y = (c - (a-b))*(c + (a-b)) / 4, then Area Δ = √((ab-y)*y)

Tried all Kahan's example (Table 1) with above Y formula (SSS => area):

(10, 10, 10) => 43.30127019
(100000, 99999.99979. 0.00029) => 9.9999 99989
(100000, 100000, 1.00005) => 52002.50002
(15000, 10000, 5000.000001) => 612.37 24357

(99999.99996, 99999.99994, 0.00003) => 1.1180 33988
(200000, 99999.99999, 99999.99999) => Error
(99999.99996, 94721.35941, 5278.64055) => 0
(200004, 100002, 100002) => 0
(31622.77662, 31622.77661, 0.000023) => 0.3274 90458
(31622.77662, 31622.77661, 0.0155555) => 245.95 40000

Edit: this is the HP-12C code for above tests (order does not matter):
Example: 2 Enter 3 Enter 4 R/S => 2.904737510

Code:

X≤Y
X<>Y
STO 0
R↓
X≤Y
X<>Y
STO* 0
R↓
R↓
CLX
+
-
-
X<>Y
Lst-X
+
*
4
/
RCL 0
X<>Y
-
Lst-X
*
√X
GTO 00