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Estimate the area of a 7-sided heptagonal plot from its seven side lengths. Cyclic-polygon method.
Construction
Generated on August 22, 2026
Plot Shape (7 sides — cyclic polygon, max-area assumption)
Estimate the area of a 7-sided heptagonal plot from its seven side lengths. Cyclic-polygon method.
A 7-sided (heptagonal) plot area calculator estimates the area of a seven-sided land parcel from its seven side lengths using the cyclic-polygon method. Heptagonal plots are rare in conventional housing but do occur — typically when a regular plot has had multiple corners clipped for easements (drains, transformers, road widening), in agricultural land bounded by multiple natural features (canal, ridge, slope, road), in heritage neighborhoods with organic non-rectangular geometry, and in modern parametric architectural schemes. Since seven side lengths do not uniquely determine a heptagon, the calculator returns the cyclic-heptagon area as the maximum-possible-area surveying default; for legal precision on highly irregular plots, demand triangulation from a licensed surveyor.
Formula
Cyclic 7-gon: solve for circumradius R such that Σᵢ 2·arcsin(sᵢ/2R) = 2π; then Area = ½·R²·Σᵢ sin(2·arcsin(sᵢ/2R))Heptagonal (seven-sided) plots are the rarest of the irregular plot shapes in Pakistani real estate — most people will go their whole lives without seeing one. But when you inherit a multi-corner agricultural plot in canal-belt Punjab, or buy a residential plot in an older neighbourhood where three corners have been clipped over the decades for drains, transformers, and road widening, you suddenly need this exact calculation and no dealer in the area can do it for you. Seven side lengths alone do not pin down a unique heptagon (the shape can flex into many configurations), so this calculator uses the cyclic-polygon method to give you the maximum possible area for those sides — accurate within 2 to 4 percent for nearly-regular heptagons, and as much as 8 to 15 percent off for highly irregular ones. Run your seven sides through and you get area in square feet, Marla (with your scheme's Marla-size), Kanal, and acres. Honest take: use this calculator for the initial valuation and to verify what the dealer is claiming. For the legal paperwork and the price-per-Marla negotiation, demand a Patwari-certified triangulated demarcation — that is the only number that will hold up in court if a dispute arises. Heptagonal plots typically sell 8 to 15 percent below the rectangular rate per Marla, so factor the discount when comparing — and never pay rectangular rates for a heptagonal plot just because the dealer rounded charitably.
A 7-sided (heptagonal) plot area calculator estimates the area of a seven-sided land parcel from its seven side lengths using the cyclic-polygon method. Heptagonal plots are rare in conventional housing but do occur — typically when a regular plot has had multiple corners clipped for easements (drains, transformers, road widening), in agricultural land bounded by multiple natural features (canal, ridge, slope, road), in heritage neighborhoods with organic non-rectangular geometry, and in modern parametric architectural schemes. Since seven side lengths do not uniquely determine a heptagon, the calculator returns the cyclic-heptagon area as the maximum-possible-area surveying default; for legal precision on highly irregular plots, demand triangulation from a licensed surveyor.
Seven-sided polygons have 4 degrees of geometric freedom beyond the side lengths. The cyclic heptagon (all seven vertices on a circle) is the maximum-area configuration. The calculator numerically solves for the circumradius R that makes the seven central angles sum to exactly 360°, then computes the total area as the sum of seven isosceles triangles. For regular heptagons (all sides equal length s), Area = (7/4) · s² · cot(π/7) ≈ 3.634 · s².
Sample 7-sided plot configurations with cyclic-heptagon area in standard Pakistani units.
| Sides (ft) | Cyclic Sq ft | Marla | Kanal | Acre |
|---|---|---|---|---|
| 30 × 30 × 30 × 30 × 30 × 30 × 30 (regular) | 3,270 | 12.02 | 0.601 | 0.0751 |
| 40 × 40 × 40 × 40 × 40 × 40 × 40 (regular) | 5,815 | 21.38 | 1.069 | 0.1335 |
| 50 × 50 × 50 × 50 × 50 × 50 × 50 (regular) | 9,085 | 33.40 | 1.670 | 0.2086 |
| 30 × 40 × 35 × 50 × 40 × 30 × 25 | 4,790 | 17.61 | 0.881 | 0.110 |
| 60 × 55 × 60 × 50 × 40 × 35 × 30 | 8,830 | 32.46 | 1.623 | 0.203 |
| 70 × 70 × 70 × 70 × 70 × 70 × 70 (regular) | 17,800 | 65.44 | 3.272 | 0.409 |
| 80 × 90 × 100 × 75 × 65 × 80 × 70 | 19,930 | 73.27 | 3.664 | 0.458 |
A 1-Kanal regular heptagonal plot is striking but rare — usually appears in modernist parametric schemes.
Agricultural heptagons of 1+ acre often result from canal-belt multi-feature boundaries.
Cumulative-easement heptagons typically lose 8–15% of buildable area vs the original 4-sided shape.
Heritage-area heptagons in older Lahore and Karachi neighborhoods are commonly 5–15 Marla.
A regular heptagonal plot with each side 40 ft has area ≈ 5,815 sq ft ≈ 21.38 Marla ≈ 1.07 Kanal.
An agricultural heptagon 80 × 90 × 100 × 75 × 65 × 80 × 70 ft cyclic area ≈ 19,930 sq ft ≈ 0.46 acres.
A heritage-area heptagon 30 × 40 × 35 × 50 × 40 × 30 × 25 ft cyclic area ≈ 4,790 sq ft ≈ 17.61 Marla.
Multi-easement plot 60 × 55 × 60 × 50 × 40 × 35 × 30 ft cyclic area ≈ 8,830 sq ft ≈ 32.46 Marla.
Large irregular farm 200 × 180 × 220 × 250 × 190 × 160 × 200 ft cyclic area ≈ 84,500 sq ft ≈ 1.94 acres.
Modern parametric heptagonal pavilion: 70 × 70 × 70 × 70 × 70 × 70 × 70 ft (regular) = 17,800 sq ft ≈ 65.4 Marla ≈ 3.27 Kanal.
Jump to a ready-made conversion — useful for quick reference and sharing:
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