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Estimate the area of a 6-sided hexagonal plot from its six side lengths. Cyclic-polygon method with Marla, Kanal, Acre conversion.
Construction
Generated on May 23, 2026
Plot Shape (6 sides — cyclic polygon, max-area assumption)
Estimate the area of a 6-sided hexagonal plot from its six side lengths. Cyclic-polygon method with Marla, Kanal, Acre conversion.
A 6-sided (hexagonal) plot area calculator estimates the area of a hexagonal land parcel from its six side lengths using the cyclic-polygon method. Hexagonal plots are uncommon in conventional grid-based housing schemes but appear at four-road junctions where two opposite corners are chamfered, in cul-de-sac plots within radial street patterns, in older organic settlements in Lahore's walled city or Karachi's old town, in agricultural land bounded by multiple canals/ridges, and in modernist 'parametric' housing schemes that intentionally break the grid for aesthetic and traffic-flow reasons. Because six side lengths alone do not determine a unique hexagon, the calculator returns the cyclic-hexagon area — the maximum possible area for those sides — as the standard surveying convention.
Formula
Cyclic 6-gon: solve for circumradius R such that Σᵢ 2·arcsin(sᵢ/2R) = 2π; then Area = ½·R²·Σᵢ sin(2·arcsin(sᵢ/2R))Hexagonal plots are uncommon in conventional Pakistani housing but they do exist — and when they do, the standard 4-sided calculator is useless and most dealers do not know how to value them properly. You will find them at four-road junctions where two opposite corners have been chamfered for visibility, in cul-de-sac plots inside radial street patterns (some newer DHA and Bahria phases use this), in older organic settlements where roads meander rather than form a grid, and on agricultural land bounded by multiple canals or ridges. Six side lengths alone do not determine a unique hexagon — the shape can flex into many configurations — so this calculator uses the cyclic-polygon method to compute the area as if all six corners lay on a single circle. That gives the maximum possible area and the standard surveying-industry estimate. For nearly-regular hexagons the answer is within 2 to 3 percent of true; for highly irregular ones the overestimate can reach 12 percent. Honest take: use this calculator to verify what the dealer is claiming and to get a Marla figure that is not wildly wrong. For the legal transfer paperwork, demand a Patwari-certified demarcation with three diagonals measured — that triangulation produces an exact answer and is what any future property dispute will be decided on. Hexagonal cul-de-sac plots in radial schemes are often the most premium plots in the scheme due to the privacy advantage; do not assume the irregularity equals discount.
A 6-sided (hexagonal) plot area calculator estimates the area of a hexagonal land parcel from its six side lengths using the cyclic-polygon method. Hexagonal plots are uncommon in conventional grid-based housing schemes but appear at four-road junctions where two opposite corners are chamfered, in cul-de-sac plots within radial street patterns, in older organic settlements in Lahore's walled city or Karachi's old town, in agricultural land bounded by multiple canals/ridges, and in modernist 'parametric' housing schemes that intentionally break the grid for aesthetic and traffic-flow reasons. Because six side lengths alone do not determine a unique hexagon, the calculator returns the cyclic-hexagon area — the maximum possible area for those sides — as the standard surveying convention.
Six-sided polygons have 3 degrees of geometric freedom beyond the side lengths — they can flex into many different shapes. The cyclic hexagon (all six vertices on a circle) is the maximum-area configuration, and is the standard convention used by Pakistani surveyors when only side lengths are available. The calculator solves numerically for the circumradius R that makes the six central angles sum to 360°, then computes the area as the sum of six isosceles triangles (each formed by one side and the center). For regular hexagons (all six sides equal), the formula simplifies to Area = (3√3/2) · s² ≈ 2.598 · s².
Sample 6-sided plot configurations with cyclic-hexagon area in standard Pakistani units.
| Sides (ft) | Cyclic Sq ft | Marla | Kanal | Acre |
|---|---|---|---|---|
| 30 × 30 × 30 × 30 × 30 × 30 (regular) | 2,338 | 8.60 | 0.430 | 0.0537 |
| 40 × 35 × 50 × 40 × 35 × 50 | 4,250 | 15.62 | 0.781 | 0.0976 |
| 50 × 50 × 50 × 50 × 50 × 50 (regular) | 6,495 | 23.88 | 1.194 | 0.149 |
| 60 × 50 × 60 × 50 × 30 × 30 | 8,920 | 32.79 | 1.640 | 0.205 |
| 80 × 70 × 80 × 70 × 60 × 60 | 16,460 | 60.52 | 3.026 | 0.378 |
| 100 × 120 × 90 × 110 × 80 × 100 | 23,510 | 86.43 | 4.322 | 0.540 |
A 1-Kanal regular hexagonal plot is a striking modernist residential format — uncommon but premium.
Hexagonal cul-de-sac plots in radial schemes are typically 5–10 Marla and command premium pricing.
Lahore walled city hexagons are usually under 1 Kanal due to dense pre-modern geometry.
Hexagonal commercial pavilions (food courts, exhibition halls) are popular at 2–4 Kanal sizes for their interior space efficiency.
A regular hexagonal plot (all six sides 50 ft) has area 6,495 sq ft ≈ 23.88 Marla ≈ 1.19 Kanal — a notable luxury residential format.
A four-road-junction hexagon with two chamfered corners 60 × 50 × 60 × 50 × 30 × 30 ft has cyclic area ≈ 8,920 sq ft ≈ 32.79 Marla.
An irregular agricultural hexagon 100 × 120 × 90 × 110 × 80 × 100 ft cyclic area ≈ 23,510 sq ft ≈ 0.54 acres.
A cul-de-sac plot with 6 sides 40 × 35 × 50 × 40 × 35 × 50 ft cyclic area ≈ 4,250 sq ft ≈ 15.62 Marla.
Hexagonal-pattern luxury hexagons in modernist schemes typically sit at 1–2 Kanal range.
Walled-city hexagons in Lahore's old town often measure under 1 Kanal due to dense organic geometry.
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