Independent Area Calculation — Yellow Zone (B3)

Date: 2026-03-04 | Version: v03 (PNG-VERIFIED) | Author: Claude (Opus 4.6) LOCKED — CURRENT

v03: Column positions SHIFTED +39cm east. Correct positions: COL-WEST center (3.64, 1.36), COL-EAST center (7.57, 1.33), partially embedded in east wall (~50cm past, ~10cm visible).
v02 CORRECTION: North wall is 860 cm, not 614.8 cm. Room WIDENS going north.
Previous v01 had the diagonal direction wrong. Corrected per MediaVerse.pdf dimensioned drawing.

Source Data (AUTHORITATIVE)

Primary: Source/2026-03-04_Final-Layouts-04-03-2026.dxf — Authoritative DXF (2026-03-04)
Cross-ref: Source/2026-03-04_MediaVerse-Reference.png — Obai’s dimensioned plan
Extraction: Source/2026-03-04_DXF-Extraction-Report.md — Full DXF analysis
All dimensions in centimeters (cm) unless noted

Extracted Dimensions from PDF (LOCKED — SSOT)

Horizontal Measurements (East-West)

South wall (bottom): 737 cm
North wall (top): 860 cm
Column row internal: 334 + 60 + 333 = 727 cm (structural spans, does NOT represent full width)
10 cm: gap annotation near east wall (wall thickness to server room B313)

Vertical Measurements (North-South)

East wall: 431 cm total height
Internal split: 111 cm (south to column row) + 50 cm (column depth) + 270 cm (column to north) = 431 cm ✓

NW Diagonal Wall

448 cm diagonal length
This is the building’s angled northwest facade
The diagonal extends OUTWARD (west) going from south to north → room WIDENS northward

Shape Analysis

The yellow zone is a RIGHT TRAPEZOID:

Two parallel sides: South (737 cm) and North (860 cm)
One perpendicular side: East wall (431 cm)
One angled side: NW diagonal (448 cm)
Right angles at SE and NE corners

Vertex Coordinates (origin at SW corner)

Point	X (cm)	Y (cm)	Description
SW	0	0	South wall, west end (diagonal base)
SE	737	0	South wall, east end
NE	737	431	North wall, east end
NW	-123	431	North wall, west end (diagonal top)

Note: NW corner extends 123 cm WEST of SW corner origin.

Diagonal Verification

Given: Diagonal = 448 cm, connecting SW (0,0) to NW (-123, 431)

Calculated diagonal: √(123² + 431²) = √(15,129 + 185,761) = √200,890 = 448.2 cm ≈ 448 cm ✓

Also verified: North − South = 860 − 737 = 123 cm = horizontal component of diagonal ✓

Area Calculation

Method: Trapezoid Formula

Area = ½ × (b₁ + b₂) × h

Where:

b₁ = South wall = 737 cm
b₂ = North wall = 860 cm
h = East wall (perpendicular height) = 431 cm

Area = ½ × (737 + 860) × 431
Area = ½ × 1,597 × 431
Area = 344,153.5 cm²
Area = 34.42 m²

Cross-check: Shoelace Formula

Vertices: SW(0,0), SE(737,0), NE(737,431), NW(-123,431)

Σ(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ):

(0×0 − 737×0) = 0
(737×431 − 737×0) = 317,647
(737×431 − (−123)×431) = 317,647 + 53,013 = 370,660
(−123×0 − 0×431) = 0

Area = ½ × |0 + 317,647 + 370,660 + 0| = ½ × 688,307 = 344,153.5 cm² = 34.42 m² ✓

Width Formula (CORRECTED)

The room WIDENS going north. At distance Y from the south wall:

Width(Y) = 7.37 + (Y / 4.31) × 1.23 meters

Y from south (m)	Width E-W (m)	Notes
0.00	7.37	South wall
0.50	7.51	—
1.00	7.66	—
1.11	7.69	Column row
1.50	7.80	—
2.00	7.94	—
2.50	8.08	—
3.00	8.23	—
3.50	8.37	—
4.00	8.51	—
4.31	8.60	North wall

Volume

Gross area: 34.42 m²
Ceiling to slab: 350 cm = 3.50 m
Raw volume: 34.42 × 3.50 = 120.5 m³
Effective height (after floating floor −15cm, acoustic ceiling −20cm): 315 cm = 3.15 m
Effective volume: 34.42 × 3.15 = 108.4 m³

Column Positions (PNG-VERIFIED 2026-03-04)

Column	Size (cm)	Center (m)	Zone Faces (cm from SW)	Notes
COL-WEST	60 × 50	(3.64, 1.36)	W:334 E:394 S:111 N:161	In-zone structural column
COL-EAST	60 × 55	(7.57, 1.33)	W:727 E:787 S:106 N:161	Partially embedded in east wall (~50 cm past, ~10 cm visible)

Column north faces aligned at Y=1.61m (161 cm from south wall)
COL-EAST extends 5 cm further south than COL-WEST (55cm vs 50cm depth)
COL-WEST east → COL-EAST west: 333 cm (clear span, SHIFTED +39cm east)
COL-EAST east face at 787 cm → extends 50 cm past east wall (737 cm); ~10 cm visible inside room
Gap to north wall: 270 cm (both columns aligned at north face)

Comparison with Other LLM Estimates

Source	Area	Comment
This calculation (v03)	34.42 m²	Trapezoid with correct 860cm north wall, PNG-verified columns
Previous v01	29.13 m²	WRONG — used 614.8cm north (diagonal direction error)
Claude Web	26.75 m²	Underestimate
ChatGPT	~33 m²	Close approximation
Gemini brief	37 m²	Overestimate
Grok Session 1	39.5 m²	Overestimate

34.42 m² is the AUTHORITATIVE value per the dimensioned PDF drawing.

STATUS: LOCKED ✓

✓ North wall dimension confirmed from PDF: 860 cm
✓ Diagonal direction confirmed: extends OUTWARD (west) going north
✓ Trapezoid area verified by both formula and shoelace: 34.42 m²
✓ Volume calculated with corrected 3.50m ceiling: 120.5 m³ raw / 108.4 m³ effective
✓ Width formula corrected: room WIDENS northward

Column positions PNG-verified. Refer to SSOT-GEOMETRY.md for locked reference values.