Four unequal sides with a diagonal
Plot Area
0
m²
Split the plot with a diagonal
Quadrilateral ABCD = △ABC + △ACD
= AB 0, BC 0, CD 0, DA 0, AC 0 m
= Two triangles with all three sides known
One diagonal is enough for a four-sided plot; for five or six sides, take one diagonal from the same corner to every other corner.
Triangle ABC — half perimeter
s₁ = (AB + BC + AC) / 2
= (0 + 0 + 0) / 2
= 0 m
Triangle ABC — Heron's formula
A₁ = √[s₁(s₁ − AB)(s₁ − BC)(s₁ − AC)]
= √[0 × 0 × 0 × 0]
= 0 m²
Triangle ACD — half perimeter
s₂ = (AC + CD + DA) / 2
= (0 + 0 + 0) / 2
= 0 m
Triangle ACD — Heron's formula
A₂ = √[s₂(s₂ − AC)(s₂ − CD)(s₂ − DA)]
= √[0 × 0 × 0 × 0]
= 0 m²
Total plot area
A = A₁ + A₂
= 0 + 0
= 0 m² = 0 sq ft = 0 cents
Cross-check on site
Re-measure the other diagonal BD and compute again
= △ABD + △BCD should give the same total
= Difference should be under 1% — anything more means a tape error
Always record which corner the diagonal was taken from on the sketch.
Method used: Triangulation by Heron's formula — survey practice for four-sided irregular plots
No plot is a perfect rectangle. A four-sided plot is split by one diagonal into two triangles, and each triangle's area is found from its three sides by Heron's formula, A = √[s(s−a)(s−b)(s−c)] where s is half the perimeter. Measure the four sides and one diagonal on site with a tape; the diagonal is what fixes the shape, without it the same four sides can enclose many different areas.
Estimates for guidance only. Confirm quantities with your site engineer.
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