**HP 20S and 21S: Heron’s Triangle**

**Introduction**

The following program calculates the area of a triangle knowing the three lengths. The area is determined by Heron’s formula:

Area: √(s * (s – a) * (s – b) * (s – c)) where s = (a + b + c)/2

Store the lengths of the triangle in registers R0, R1, and R2 respectively.

Results are stored in the following registers:

R3: s

R4: area

**HP 20S and 21S Program: Heron’s Triangle**

The key codes for both calculators are the same.

STEP KEY KEY CODE

01 LBL A 61, 41, A

02 RCL 0 22, 0

03 STO 3 21, 3

04 RCL 1 22, 1

05 STO+3 21, 75, 3

06 RCL 2 22, 2

07 STO+3 21, 75, 3

08 2 2

09 STO÷3 21, 45, 3

10 RCL 3 22, 3

11 STO 4 21, 4

12 RCL 3 22, 3

13 – 65

14 RCL 0 22, 0

15 = 74

16 STO×4 21, 55, 4

17 RCL 3 22, 3

18 – 65

19 RCL 1 22, 1

20 = 74

21 STO×4 21, 55, 4

22 RCL 3 22, 3

23 – 65

24 RCL 2 22, 2

25 = 74

26 STO×4 21, 55, 4

27 RCL 4 22, 4

28 √ 11

29 STO 4 21, 4

30 RTN 61, 26

**Example**

R0 = 17, R1 = 18, R2 = 21. Result: Area: 148.833238744

Note: I switched computers last week. For the last few years, I used Microsoft Word but for the time being I am going to use WordPad. Let’s see how this goes. Fortunately I can still can use Unicode characters with Alt+X. For example, I can type 221A, then type [Alt] + [ X ] to get the square root character. Unfortunately, WordPad doesn’t have spell check.

Eddie

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