Area and Volume Formulation

Menu-driven geometry reference tool that calculates surface area and volume for five solid shapes: cube, rectangular block (labelled “rectangle”), triangle/prism, cylinder, and sphere. The user selects a shape by pressing keys 1–5, and the program uses a computed GOTO (`GOTO VAL Y$*1000`) to jump directly to the appropriate calculation routine at lines 1000, 2000, 3000, 4000, or 5000. The triangle section applies Heron’s formula to derive the altitude and then the area, and also outputs prism volumes for each of the three sides as the length. The program makes extensive use of inverse-video text (the `%X` sequences) for menu highlighting and prompts, and uses `FAST`/`SLOW` mode switching around input sections for display speed control on the ZX81.

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Program Analysis

Program Structure

The program is organized as a top-level menu at lines 100–330, followed by five independent calculation routines, a shared exit/restart block at lines 9000–9020, and save/stop utilities at 9997–9999.

Line range	Purpose
0	Program title line (FAST/display artifact, not executed)
100–290	Main menu display
300–350	Key input and validation loop
1000–1060	Cube: surface area and volume
2000–2150	Rectangular block: surface area and volume
3000–3940	Triangle/prism: Heron’s formula, area, three prism volumes, invalid input trap
4000–4080	Cylinder: surface area and volume using PI
5000–5060	Sphere: surface area and volume using PI
9000–9020	Shared “press RETURN” pause and restart
9997–9999	STOP, SAVE, and loop-back utilities

Key BASIC Idioms

• Computed GOTO: Line 350 uses GOTO VAL Y$*1000 to dispatch to the correct routine based on the digit key pressed (1–5 → lines 1000–5000). This is a classic ZX81 memory-saving technique, avoiding a chain of IF statements.
• Input validation via character codes: Line 320 checks CODE Y$<29 OR CODE Y$>33. On the ZX81, the character codes for digits 1–5 are 29–33, so this neatly accepts only valid menu choices without string comparison.
• FAST/SLOW switching: FAST is used during screen drawing (lines 100, 330) and SLOW before INPUT statements (lines 290, 1005, 2005, 3005, 4005, 5010) to ensure stable video during user interaction.
• PAUSE 40000 as keypress wait: Lines 3920 and 9010 use PAUSE 40000 (approximately 40 seconds) as a long pause to hold the display, functioning as an effective “press any key” wait.
• Inverse video with %X: Menu labels, prompts, and result headings use inverse-video characters extensively for visual emphasis.

Geometry Calculations

Shape	Surface Area Formula	Volume Formula
Cube	6·S²	S³
Block	2·S1·S2 + 2·S2·S3 + 2·S1·S3	S1·S2·S3
Triangle (area only)	Heron’s formula → AR	AR·S1, AR·S2, AR·S3 (three prism depths)
Cylinder	2·π·R² + 2·π·R·L	π·R²·L
Sphere	4·π·R²	(4·π·R³)/3

Triangle Routine and Heron’s Formula

Lines 3070–3130 implement a two-step derivation. First, the semi-perimeter is computed: S=(S1+S2+S3)/2. A validity check at line 3080 (IF S<=S1) catches degenerate cases where the longest side equals or exceeds the semi-perimeter (i.e., triangle inequality violation), jumping to the error handler at line 3900.

The altitude Y3 is derived from Heron’s formula rearranged to give the height relative to side S1. Line 3110 then applies ATN to compute an angle, though this value (A) is computed but never used in any subsequent output — it appears to be a vestigial calculation left over from an earlier version of the code that may have displayed the angle.

The area AR = (S1·Y3)/2 (base × height / 2) is then used to print both the triangle area and three prism volumes (AR multiplied by each side as the prism depth). This is a creative extension beyond the other shapes.

Notable Techniques and Anomalies

• Unused variable: Variable A (the arctangent calculation at lines 3100–3110) is assigned but never printed or used further. This is a harmless dead-code remnant.
• Mislabelled shape: The menu calls option 2 “RECTANGLE” but the routine calculates a rectangular block (cuboid), correctly prompting for three distinct side lengths.
• Triangle label inconsistency: The menu labels option 3 “TRIANGLE” but the output section also prints prism volumes, making it implicitly a triangular prism calculator as well.
• Line 300 double-print trick: The prompt at line 300 is printed twice in succession — first in inverse video, then immediately overwritten in normal video at the same AT position. This creates a normal-video prompt while avoiding a CLS that would clear the menu.
• Exponentiation notation: The program uses ** for exponentiation throughout, standard ZX81 BASIC.