Geometry and Measurement
Find the area from base and perpendicular height, or use all three sides when no altitude is known.
With a base b and perpendicular height h, area A = bh/2. A base of 10 m and perpendicular height of 4 m give A = 20 m². The height is not generally a sloping side; it is the shortest straight distance from the opposite vertex to the base line.
If only sides a, b, and c are known, calculate semiperimeter s = (a + b + c)/2 and then use Heron’s formula A = √[s(s−a)(s−b)(s−c)]. For sides 3 m, 4 m, and 5 m, s = 6 m and A = √[6 × 3 × 2 × 1] = 6 m². No right-angle assumption is needed.
Three positive lengths form a nondegenerate triangle only when the sum of the two shorter sides exceeds the longest. Lengths 1, 2, and 3 fail because 1 + 2 = 3: they lie in a straight line, with zero area. The calculator removes the previous answer when the dimensions are invalid.
Input lengths are converted to meters, then squared for area. That is why converting a length by 100 from meters to centimeters converts the numerical area by 10,000. For example, 6 m² = 60,000 cm². Square feet and square inches are based on exact foot and inch definitions. Results assume straight edges and planar geometry; field measurements can add uncertainty.
| Item | Meaning | Check |
|---|---|---|
| Input method | Base-height or three sides | Values remain in their own method when switching. |
| Height | Perpendicular distance to the base line | A sloping edge is not a substitute. |
| Side lengths | The three edges used by Heron’s formula | The two shorter lengths must exceed the longest when added. |
| Area unit | Squared unit for the final answer | Output unit can differ from input length unit. |
Estimate a triangular section from a base and surveyed perpendicular offset.
Estimate face area for a straight-edged triangular piece before seam allowance.
Find area when altitude is inconvenient but all sides are available.
The tool does not subtract holes or account for curved boundaries, terrain slope, or material waste.
Only if that side is perpendicular to the chosen base. Otherwise measure the altitude or use three side lengths.
It is half the perimeter: (a + b + c)/2. Heron’s formula uses it to compute area from three sides.
At least one length is nonpositive, or the two shorter sides do not add to more than the longest side.
Area is measured in square units, so the length conversion factor of 100 is squared.
Last reviewed: October 23, 2026. Calculations run in your browser. Confirm dimensions and units for consequential work.
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