Area – Geometry

This program calculates the area of seven geometric shapes: circle, sphere (surface area), parabola, triangle, square, rectangle, and ellipse. After prompting the user to enter a shape name, it branches to the appropriate input routine using a series of conditional GOTOs, then computes and displays the result before looping back for another calculation. The sphere surface area (4πr²) and circle area (πr²) share a single code path, distinguished by checking the first character of the input string with X$(1). The ellipse area uses the approximation 0.7854×J×N, where 0.7854 ≈ π/4, effectively computing π×(J/2)×(N/2) treating J and N as full axes rather than semi-axes.

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Program Analysis

Program Structure

The program is organized as a menu-driven loop. Lines 5–15 display a title, lines 100–180 handle shape selection and dispatch, lines 200–560 contain per-shape input and calculation routines, and line 600 is a shared output section that prints the result and loops back to the menu.

Lines	Purpose
5–15	Title display
100–180	Shape input, branching dispatcher, fallback loop
200–250	Circle / Sphere handler
300–380	Parabola / Triangle handler
400–470	Square / Rectangle handler
500–560	Ellipse handler
600–620	Shared output and loop-back

Branching and Shape Dispatch

Shape pairs are routed to a single shared subroutine using compound OR conditions on lines 140–160. Within each shared routine, the first character of X$ is tested with X$(1) to select the appropriate formula — for example, IF X$(1)="S" to distinguish Sphere from Circle, and IF X$(1)="P" vs IF X$(1)="T" for Parabola and Triangle. This avoids duplicating input prompts for shape pairs that require the same inputs (radius, or base and height).

Mathematical Formulas Used

• Circle: A = PI * (R**2) — standard πr²
• Sphere (surface area): A = 4 * PI * (R**2) — computed by multiplying the circle result by 4
• Parabola (segment area): A = B * H * 2/3 — correct formula for a parabolic segment
• Triangle: A = B * H * .5 — standard ½ × base × height
• Square / Rectangle: A = L * W — for a square, the user is expected to enter equal width and length
• Ellipse: A = .7854 * J * N — uses the constant 0.7854 ≈ π/4

Notable Techniques

The use of PI as a built-in keyword provides full floating-point precision for circular calculations. The exponentiation operator ** is used for squaring the radius. The ellipse approximation constant 0.7854 (= π/4) is a classic shortcut — when J and N represent the full major and minor axes, the formula π/4 × J × N equals π × (J/2) × (N/2), which is the correct ellipse area formula using semi-axes. This is mathematically correct provided the user supplies full-axis values.

Bugs and Anomalies

The Square handler on lines 400–470 does not distinguish between squares and rectangles — it simply computes L * W for both. A square requires only one dimension, but the program still prompts for both width and length; a user entering a square must input the same value twice. Additionally, line 460 (LET A=L*W) unconditionally sets A regardless of which shape was selected, unlike the Parabola/Triangle branch which uses conditional assignments on lines 360–370 — this means no first-character check is needed or performed for the square/rectangle pair, which works correctly here since the formula is identical for both.

If the user enters an unrecognised shape name, line 180 loops back to line 100, but there is no error message to inform the user their input was invalid — the program silently re-displays the prompt.