Plot Area Calculator (5-Sided / Pentagonal)
Estimate the area of a 5-sided pentagonal plot from its five side lengths. Cyclic-polygon method.
Construction
Plot Area Calculator (5-Sided / Pentagonal)
Generated on April 29, 2026
Plot Shape (5 sides — cyclic polygon, max-area assumption)
Plot Pricing — convert any rate to all others
?What is the Plot Area Calculator (5-Sided / Pentagonal)?
A 5-sided (pentagonal) plot area calculator estimates the area of a five-sided land parcel from its five side lengths. Pentagonal plots arise naturally in Pakistani and South Asian real estate at three-road corners (where one corner is chamfered for visibility), at irregular T-junctions, in housing schemes with non-90° master-plans, in agricultural land bounded by canals or natural slopes, and in plots where one corner has been clipped for an easement, drain, or transformer pad. Because five side lengths alone do not uniquely determine a pentagon (an infinite family of pentagons share the same side lengths but flex into different shapes), this calculator uses the cyclic-polygon method — the unique pentagon whose vertices all lie on a circle — which yields the maximum possible area. Use it for initial estimation; for legal precision on irregular pentagons, divide the shape into triangles using diagonals.
The Formula
When a polygon has more than 4 sides and only the side lengths are known, no single formula gives a unique area — the same sides can flex into many shapes. The mathematical convention is to compute the cyclic polygon area: assume all five vertices lie on a single circle (the maximum-area case for those sides). Numerically, solve for the circle's radius R such that the sum of central angles around each side equals 360°, then sum the area of the five triangles formed by each side and the center. This is a generalization of Brahmagupta's formula for cyclic quadrilaterals. The area is exact for cyclic pentagons and an upper bound for non-cyclic ones; surveyors prefer this conservative approach to triangulation when diagonals are unmeasured.
Common Pentagonal Plot Areas (cyclic estimate, 272 sq ft Marla)
Sample 5-sided plot configurations with their cyclic-pentagon area in standard Pakistani units.
| Sides (ft) | Cyclic Sq ft | Marla | Kanal | Acre |
|---|---|---|---|---|
| 40 × 50 × 60 × 50 × 35 | 4,830 | 17.76 | 0.888 | 0.111 |
| 50 × 60 × 50 × 60 × 30 | 6,840 | 25.15 | 1.257 | 0.157 |
| 60 × 60 × 60 × 60 × 60 (regular) | 6,193 | 22.77 | 1.139 | 0.142 |
| 80 × 90 × 100 × 75 × 65 | 13,260 | 48.75 | 2.438 | 0.305 |
| 100 × 120 × 150 × 110 × 80 | 26,440 | 97.21 | 4.860 | 0.607 |
| 200 × 250 × 220 × 180 × 150 | 76,800 | 282.4 | 14.12 | 1.764 |
Put It in Perspective
A 25-Marla pentagonal corner plot is roughly the size of a luxury 1.25-Kanal home with three street frontages.
Regular pentagons (all sides equal) are rare in real estate but useful as a sizing reference.
Most chamfered corner plots in DHA, Bahria Town, and Lake City have one shorter 'cut' side of 25–35 ft on otherwise rectangular geometry.
Agricultural pentagons of 1+ acre often result from irrigation realignment in Punjab's canal-belt.
Practical Examples
A chamfered corner plot 50 × 60 × 50 × 60 × 30 ft (one corner clipped 30 ft for visibility) cyclic area ≈ 6,840 sq ft ≈ 25.1 Marla.
A pentagonal lot 80 × 90 × 100 × 75 × 65 ft cyclic area ≈ 13,260 sq ft ≈ 48.7 Marla ≈ 2.44 Kanal.
An irrigation-bounded pentagon 100 × 120 × 150 × 110 × 80 ft cyclic area ≈ 26,440 sq ft ≈ 0.61 acres.
Regular pentagon (all five sides 60 ft) area = 6,193 sq ft ≈ 22.77 Marla — useful as a reference baseline.
T-junction pentagon 40 × 50 × 60 × 50 × 35 ft cyclic area ≈ 4,830 sq ft ≈ 17.76 Marla.
Agricultural pentagon 200 × 250 × 220 × 180 × 150 ft cyclic area ≈ 76,800 sq ft ≈ 1.76 acres.
Frequently Asked Questions
Popular Conversions
Jump to a ready-made conversion — useful for quick reference and sharing: