Averaging methodApproximate
Area ≈ ((AB + CD) / 2) × ((BC + DA) / 2)
Land measurement formulas, complete collection
Choose the right formula by understanding the shape of the land. Each diagram uses English point labels A, B, C, D, etc.—so it is easy to match them with how measurements are written in the field or on a map.
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Which formula to use when?
Choose the path below based on the land's shape and the measurements you have.
Triangle — three sides known
Use Heron's formula. If the base and perpendicular height are known, ½ × base × height is simpler.
Irregular four-sided plot — one diagonal known
Split it into two triangles with the diagonal and add the two areas. This is more reliable than simply averaging the four sides.
Four sides known, but no diagonal/angle
The actual area cannot be determined uniquely. Do not treat an approximate or maximum-possible result as the exact measurement; if possible, measure one diagonal.
Irregular or many-sided plot
Draw diagonals from a convenient point to split the plot into triangles, find each area and add them up at the end.
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1. Basic units of measurement
Quick reference for the standard values used in Bangladesh. Local katha/bigha values can differ by region.
Decimals and square feet
1 decimal435.6 square feet
1 acre100 decimals
100 decimals1 acre
Katha and bigha
1 katha720 square feet
20 katha1 bigha
1 bigha≈ 33.06 decimals
Chain and link
1 chain66 feet
1 chain100 links
1 link0.66 feet
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2. Four-sided plot: averaging method vs diagonal method
On an irregular four-sided plot, multiplying only the averages of opposite sides gives an approximate result. Measuring one diagonal and splitting the plot into two triangles is far more reliable.
Split by diagonal ACAccurate method
Area = Heron(AB, BC, AC) + Heron(AC, CD, DA)
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3. Formulas for triangular plots
Heron's formula when all three sides are known; for a right triangle, the base × height method is simplest.
3.1 Three sides known — Heron's formula
Most widely usables = (a + b + c) / 2
Area = √[s(s−a)(s−b)(s−c)]
Here a = BC, b = CA and c = AB.
3.2 Right triangle
Area = 0.5 × AB × AC
If the angle at A is 90°, AB = height and AC = base.
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4. Trapezium — plot with two parallel sides
If AB and CD are parallel, multiply half their sum by the perpendicular height h.
Area = 0.5 × (AB + CD) × h
h is the perpendicular distance between AB and CD; the length of a slanted side is not h.
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5. Rectangle and square
On a straight four-sided plot, use the side lengths with points ABCD.
Rectangle
Area = AB × BC
Perimeter: 2 × (AB + BC)
Square
Area = AB²
Perimeter: 4 × AB
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6. Parallelogram and rhombus
For a parallelogram use the base and perpendicular height; for a rhombus use the two diagonals.
Parallelogram
Area = DC × h
Rhombus
Area = 0.5 × AC × BD
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7. Circular and elliptical plots
For a circle use radius r from centre O; for an ellipse use the two semi-axes a and b.
Circle
Area = π × r²
Circumference: 2πr · π ≈ 3.1416
Ellipse
Area = π × a × b
a: Semi-major axis · b: Semi-minor axis
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8. Irregular or polygonal plots
This last method is the most important: draw diagonals from one point to split the plot into separate triangles, find the area of each triangle and add them up at the end.
- Measure the diagonals from A to C, D, E and F.
- This gives ABC, ACD, ADE, AEF, AFG—five triangles.
- For each triangle, use Heron's formula with its three sides.
- Add the areas of all the triangles to get the total land.
Total Area = T1 + T2 + T3 + T4 + T5