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Estimate the area of an 8-sided octagonal plot from its eight side lengths. Cyclic-polygon method.
Construction
Generated on May 23, 2026
Plot Shape (8 sides — cyclic polygon, max-area assumption)
Estimate the area of an 8-sided octagonal plot from its eight side lengths. Cyclic-polygon method.
An 8-sided (octagonal) plot area calculator estimates the area of an octagonal land parcel from its eight side lengths using the cyclic-polygon method. Octagonal plots, while uncommon, do appear in real estate at four-way intersections where all four corners are chamfered (a classic 'octagon plot' visibility design), in roundabout-adjacent retail/commercial sites, in modernist parametric architectural plots, in agricultural land bounded by multiple natural features, and in landmark properties where octagonal symmetry is intentional (mosques, gardens, decorative pavilions). Since eight side lengths do not uniquely determine an octagon, the calculator returns the cyclic-octagon area — the maximum possible area for those sides — using a numerical circumradius solver.
Formula
Cyclic 8-gon: solve for circumradius R such that Σᵢ 2·arcsin(sᵢ/2R) = 2π; then Area = ½·R²·Σᵢ sin(2·arcsin(sᵢ/2R))Octagonal plots split into two very different markets: prime corner commercial sites where all four corners of a rectangular plot have been chamfered for traffic visibility (a Mughal-era urban planning format that survives today in older Lahore, Multan, Peshawar, and newer Bahria/DHA roundabout sites), and rare residential plots that ended up octagonal through cumulative corner-clipping over decades. The commercial version commands premium prices — four street frontages, unmatched visibility, excellent pedestrian access from all directions. The residential version typically sells 8 to 15 percent below the per-Marla rate of nearby rectangular plots because the buildable rectangle inside is smaller. Eight side lengths alone do not pin down a unique octagon (the shape can flex into many configurations), so this calculator uses the cyclic-polygon method — accurate within 2 percent for nearly-regular octagons, up to 18 percent over for highly irregular ones. Honest take: if you are looking at a chamfered-corner commercial octagon at a four-way intersection, expect to pay a premium and budget creatively for the design. If you are evaluating a residential octagon that ended up irregular through corner clipping, demand the standard 8 to 15 percent discount per Marla and confirm via a Patwari-certified triangulated survey before transferring any meaningful money. The math is simple; the negotiation requires knowing both numbers.
An 8-sided (octagonal) plot area calculator estimates the area of an octagonal land parcel from its eight side lengths using the cyclic-polygon method. Octagonal plots, while uncommon, do appear in real estate at four-way intersections where all four corners are chamfered (a classic 'octagon plot' visibility design), in roundabout-adjacent retail/commercial sites, in modernist parametric architectural plots, in agricultural land bounded by multiple natural features, and in landmark properties where octagonal symmetry is intentional (mosques, gardens, decorative pavilions). Since eight side lengths do not uniquely determine an octagon, the calculator returns the cyclic-octagon area — the maximum possible area for those sides — using a numerical circumradius solver.
Eight-sided polygons have 5 degrees of geometric freedom beyond the side lengths. The cyclic octagon (all eight vertices on a circle) is the unique maximum-area configuration and is the standard surveying default. The calculator solves numerically for the circumradius R that makes the eight central angles sum to 360°, then sums eight triangle areas. For regular octagons (all sides equal length s), Area = 2 · (1 + √2) · s² ≈ 4.828 · s² — a useful sanity check.
Sample 8-sided plot configurations with cyclic-octagon area in standard Pakistani units.
| Sides (ft) | Cyclic Sq ft | Marla | Kanal | Acre |
|---|---|---|---|---|
| 20 × 20 × 20 × 20 × 20 × 20 × 20 × 20 (regular) | 1,931 | 7.10 | 0.355 | 0.0443 |
| 30 × 30 × 30 × 30 × 30 × 30 × 30 × 30 (regular) | 4,345 | 15.97 | 0.799 | 0.0998 |
| 40 × 40 × 40 × 40 × 40 × 40 × 40 × 40 (regular) | 7,725 | 28.40 | 1.420 | 0.1774 |
| 50 × 50 × 50 × 50 × 50 × 50 × 50 × 50 (regular) | 12,070 | 44.38 | 2.219 | 0.2772 |
| 60 × 30 × 60 × 30 × 60 × 30 × 60 × 30 | 8,700 | 31.99 | 1.599 | 0.200 |
| 70 × 50 × 70 × 50 × 70 × 50 × 70 × 50 | 14,360 | 52.79 | 2.640 | 0.330 |
| 100 × 80 × 90 × 70 × 100 × 80 × 90 × 70 | 24,140 | 88.75 | 4.438 | 0.554 |
A 30-Marla chamfered octagonal corner plot is prime retail real estate at any urban four-way intersection.
Regular octagonal mosque precincts often fall in the 1–3 Kanal range.
Decorative pavilion octagons (gardens, exhibition halls) are typically 7–15 Marla.
Agricultural octagons over 1 acre are usually canal-belt parcels with multiple natural boundaries.
A regular octagonal plot with each side 30 ft has area ≈ 4,345 sq ft ≈ 15.97 Marla — a notable retail commercial plot.
A four-way-junction octagon (4 chamfered corners) 60 × 30 × 60 × 30 × 60 × 30 × 60 × 30 ft cyclic area ≈ 8,700 sq ft ≈ 32.0 Marla.
Mosque-precinct octagon 50 × 50 × 50 × 50 × 50 × 50 × 50 × 50 ft (regular) = 12,070 sq ft ≈ 44.4 Marla ≈ 2.22 Kanal.
Agricultural irregular octagon 100 × 80 × 90 × 70 × 100 × 80 × 90 × 70 ft cyclic area ≈ 24,140 sq ft ≈ 0.55 acres.
Decorative pavilion plot 40 × 40 × 40 × 40 × 40 × 40 × 40 × 40 ft = 7,725 sq ft ≈ 28.4 Marla.
Roundabout commercial octagon 70 × 50 × 70 × 50 × 70 × 50 × 70 × 50 ft cyclic area ≈ 14,360 sq ft ≈ 52.8 Marla ≈ 2.64 Kanal.
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